Adams, W.W., Boyle, A., Loustaunau, P., Transitivity for Weak and Strong Gröbner Bases, J. Symb. Comp. 15 (1993), 49–65.
Alonso, M. E., Castro-Jimènez, F. J., Hauser, H., Encoding Algebraic Power Series arxiv.ong/pdf/1403.4104v1.pdf
Alonso, M. E., Luengo, I., Raimondo, M., An Algorithm on Quasi-Ordinary Polynomials, L. N. Comp. Sci. 357 (1989), 59–73, Springer.
Anick, D. J., On the Homology of Associative Algebras, Trans. A.M.S. 296 (1986), 641–659.
Apel, J., Gröbnerbasen in Nichetkommutativen Algebren und ihre Anwendung, Dissertation, Leipzig (1988).
Apel, J., Division of Entire Functions by Polynomial Ideals, L. N. Comp. Sci. 948 (1995), 82–958, Springer.
Apel, J., The Theory of Involuting Divisions and an Application to Hilbert Function Computations, J. Symb. Comp. 25 (1998), 683–704.
Apel, J., Computational Ideal Theory in Finitely Generated Extension Rings, T.C.S. 224 (2000), 1–33.
Apel, J., Lassner, W., An algorithm for calculations in enveloping fields of Lie algebras, In: Proc. Int. Conf. on Comp. Algebra and Its Appl. in Theoretical Physics, JINR D11-85-792, Dubna (1985), 231–241.
Apel, J., Lassner, W., Computation and Simplification in Lie Fields, L. N. Comp. Sci. 378 (1987), 468–478, Springer
Apel, J., Stückrad, J., Tworzewski, P., Winiarski, T., Reduction of Everywhere Convergent Power Series with Respect to Gröbner Bases, J. Pure Appl. Algebra 110 (1996), 113–129.
Apel, J., Stückrad, J., Tworzewski, P., Winiarski, T., Properties of Entire Functions over Polynomial Rings via Gröbner Bases, J. AAECC 14 (2003), 1–10.
Artin, M., Schelter, W., Graded Algebras of Global Dimension 3, Adv. Math. 66 (1987), 171–216.
Aschenbrenner, M., Hillar, C. J.Finite Generation of Symmetric Ideals, Trans. A.M.S. 359 (2007), 5171–5192, and Trans. A.M.S. 361 (2009), 5627.
Aschenbrenner, M., Hillar, C. J.An Algorithm for Finding Symmetric Gröbner Bases in Infinite Dimensional Ring, Proc. ISSAC'08 (2008), 117–123, ACM.
Assi, A., Standard Bases, Criticals Tropisms and Flatness, J. AAECC 4 (1993), 197–215.
Bächler, T., Gerdt, V., Lange-Hegermann, M., Robertz, D., Thomas Decomposition of Algebraic and Differentil Systems, J. Symb. Comp. 47 (2012), 1223–1266.
Bardet, M., Étude des systèmes algébriques sutdterminés. Applications aux codes correcteures et à la cryptographie, These de Doctorat, Paris6 (2004).
Barkee, B., Gröbner Bases. The Ancient Secret Mystic Power of the Algu Compubraicus. A Revelation Whose Simplicity Will Make Ladies Swoon and Grown Men Cry, Cornell University MSI Technical Report (1988).
Bayer, D., The Division Algorithm and the Hilbert Scheme, PhD Thesis, Harvard (1981).
Becker, T., Standard Bases and Some Computations in Rings of Power Series, J. Symb. Comp. 10 (1990), 165–178.
Becker, T., Standard Bases in Power Series Rings: Uniqueness and Superfluous Criterial Pairs, J. Symb. Comp. 15 (1993), 251–265.
Becker, T., Weispfenning, V., Gröbner Bases, Springer (1982).
Bergman, G. H., The Diamond Lemma for Ring Theory, Adv. Math. 29 (1978), 178–218.
Bigatti, A., Aspetti combinatorici e computazionali dell'Algebra Commutative, PhD Thesis, Genova (1995).
Bigatti, A., Upper Bounds for the Betti Numbers of a Given Hilbert Function, Communications in Algebra 21 (1993), 2317–2334.
Borges, M. A., Borges, M., Gröbner Bases Property on Elimination Ideal in the Noncommutative Case. In: Buchberger, B., Winkler, F. (Eds.), Gröbner Bases and Application (1998), Cambridge University Press, 323–337.
Borges, M. A., Borges, M., Castellanos, J.A., Martinez, E., The Symmetric Groups Given by a Gröbner Basis, J. Pure Appl. Algebra 207 (2006), 149–154.
Borges, M. A., Estrada, M. V., Gröbner Bases and G-presentations of Finite Generated Monoids (1995), preprint.
Borodin, A., On Relating Time and Space to Size and Depth, SIAM Journal on Computing 6 (1977), 733.
Borodin, A., Cook, S., Pippenger, N.Parallel Computation for Well-endowed Rings and Space-bounded Probabilistic Machines, Information and Control 58 (1983), 113–136.
Bouillet, F., Lazard, D., Ollivier, F., Petitot, M., Representation for the Radical of a Finitely Generated Differential Ideal (1996), Proc. ISSAC'95 (1995), 158–166, ACM.
Buchberger, B.Miscellaneous Results on Gröbner Bases for Polynomial Ideals II. Technical Report 83/1, University of Delaware, Department of Computer and Information Sciences, 1983. p. 31.
Bueso, J.L., Castro, F. J., Gomez Torrecilla, J., Lobillo, F. J., An Introduction to Effective Calculus in Quantum Groups. In : Caenepeel, S., Verschoren, A. (Eds.) Rings, Hopf Algebras and Brauer Groups, M. Decker (1998), 55–83.
Cartan, E., Sur l'intégration des systèmes d’équations aux différentielles totals, Ann. Éc. Norm. 3e série 18 (1901), 241.
Cartan, E., Sur la structure des groupes infinis de transformations, Ann. Éc. Norm. 3e série 21 (1904), 153.
Cartan, E., Sur les systèmes en involution d’équations aux dérivées partielles du second ordre à une fonction inconnue de trois variables indépendentes, Bull. Soc. Math. 39 (1920), 356.
Ceria, M., Roggero, M., Term-ordering Free Involutive Bases, J. Symb. Comp. 68 (2015), 87–108. http://arxiv.org/pdf/1310.0916v1.pdf
Chyzak, F., Salvy, B., Non-commutative Elimination in Ore Algebras Proves Multivariate Identities, J. Symb. Comp. 26 (1998), 187–227.
Cioffi, F., Roggero, M., Flat Families by Strongly Stable Ideals and a Generalization of Gröbner Bases, J. Symb. Comp. 46 (2011), 1070–1084.
Cohn, P. M., Noncommutative Unique Factorization Domains, Trans. A.M.S. 109 (1963), 313–331.
Cohn, P. M., Ring with a Weak Algorithm, Trans. A.M.S. 109 (1963), 332–356.
Cojocaru, S., Ufnarovski, V., Noncommutative Gröbner Basis, Hilbert Series, Anick's Resolution and BERGMAN under MS-DOS, Computer Science Journal of Moldova 3 (1995), 24–39.
Deery, T., Rev-lex Segment Ideals and Minimal Betti Numbers, Queens Papers in Pure and Applied Algebra, The Curves Seminar, vol. X (1999).
de Graaf, W. A., Wisliceny, J., Constructing Bases of Finitely Presented Lie Algebras using Gröbner Bases in Free Algebras, Proc. ISSAC'99 (1999), 37–44, ACM.
Delassus, E., Extension du théorème de Cauchy aux systèmes les plus généraux d’équations aux dérivées partielles, Ann. Éc. Norm. 3e série 13 (1896), 421–467.
Delassus, E., Sur les systèmes algébriques et leurs relations avec certains systèmes d'equations aux dérivées partielles, Ann. Éc. Norm. 3e série 14 (1897), 21–44.
Delassus, E., Sur les invariants des systèmes différentiels, Ann. Éc. Norm. 3e série 25 (1908), 255–318.
Drach, J., Essai sur la théorie général de l'integration et sur la classification des Trascendentes, Ann. Éc. Norm. 3e série 15 (1898), 245–384.
Dubé, T.W., The Structure of Polynomial Ideals and Gröbner Bases. SIAM J. Comput., 19(4) (2006), 750–773.
Eder, C., Perry, J., F5C: A Variant of Faugère's F5 Algorithm with Reduced Gröbner Bases, J. Symb. Comp. 45 (2010), 1442–1450.
Eder, C., Perry, J., Signature-based Algorithms to Compute Gröbner Bases, Proc. ISSAC'11 (2011), 99–106, ACM.
Eisenbud, D., Peeva, I., Sturmfels, B., Non-commutative Gröbner Bases for Commutative Algebras, Proc. A.M.S. 126 (1998) 687–691.
Farkas, D. R., Feustel, C. D., Green, E. L.Synergy in the Theories of Gröbner Bases and Path Algebras, Can. J. Math. 45 (1993), 727–739.
Faugère, J.-C., A New Efficient Algorithm for Computating Gröbner Bases (F4), J. Pure Appl. Algebra 139 (1999), 61–88.
Faugère, J.-C., A New Efficient Algorithm for Computating Gröbner Bases without Reduction to Zero (F5), Proc. ISSAC 2002 (2002), 75–83, ACM.
Galligo, A., Some Algorithmic Questions on Ideals of Differential Operators, L. N. Comp. Sci. 204 (1985), 413–421, Springer.
Gateva-Ivanova, T., Noetherian Properties and Growth of Some Associative Algebras, Progress in Mathematics 94 (1990), 143–158, Birkhäuser.
Gateva-Ivanova, T., On the Noetherianity of Some Associative Finitely Presented Algebras, J. Algebra 138 (1991), 13–35.
Gateva-Ivanova, T., Noetherian Properties of Skew Polynomial Rings with Binomial Relations, Trans. A.M.S. 345 (1994), 203–219.
Gateva-Ivanova, T., Skew Polynomial Rings with Binomial Relations, J. Algebra 185 (1996), 710–753.
Giesbrecht, M., Reid, G., Zhan, Y., Non-Commutative Grobner Bases in Poincare–Birkhoff–Witt Extension, The Ontario Research Centre for Computer Algebra, ORCCA Technical Report TR-03-02 (2003)
Gerdt, V. P., Involutive algorithms for computing Gröbner bases. In Computational Commutative and Non-Commutative Algebraic Geometry, Cojocaru, S., Pfister, G., Ufnarovski, V. (Eds.), NATO Science Series, IOS Press, 2005, pp. 199–225.
Gerdt, V. P., Blinkov, Y. A., Involutive Bases of Polynomial Ideals, Math. Comp. Simul. 45 (1998), 543–560.
Gerdt, V. P., Blinkov, Y. A., Minimal Involutive Bases, Math. Comp. Simul. 45 (1998), 519–541.
Gerdt, V. P., Blinkov, Y. A., Involutive Division Generated by an Antigraded Monomial Ordering, L. N. Comp. Sci. 6885 (2011), 158–174, Springer.
Gerdt, V. P., Yanovich, D.A., Effectiveness of Involutive Criteria in Computation of Polynomial Janet Bases, Programming and Computer Software 32 (2006), 134–138.
Gerdt, V. P., Zinin, M.V., A Pommaret Division Algorithm for Computing Gröbner Bases in Boolean Rings. Proceedings of ISSAC 2008, 95–102, ACM Press.
Gerritzen, L., On Non-Associative Gröbner Bases, Symposium in Honor of Bruno Buchberger's 60th Birthday, RISC-Linz, 2002.
Gerritzen, L., Tree Polynomials and Non-Associative Gröbner Bases, J. Symb. Comp. 41 (2006), 297–316.
Green, E. L., Multiplicative Bases, Gröbner Bases and Right Gröbner Bases, J. Symb. Comp. 29 (2000), 601–624.
Göbel, M., Computing Bases for Rings of Permutation-invariant Polynomials, J. Symb. Comp. 19 (1995), 258–291.
Göbel, M., Symedeal Gröbner Bases, L. N. Comp. Sci. 1103 (1996), 48–62, Springer.
Göbel, M., A Constructive Description of SAGBI Bases for Polynomial Invariants of Permutation Groups, J. Symb. Comp. 26 (1998), 261–272.
Göbel, M., On the Reduction of G-invariant Polynomials for Arbitrary Permutation Groups, Progress in Computer Science and Applied Logic 15 (1998), 35–46.
Göbel, M., The ‘Smallest’ Ring of Polynomial Invariants of a Permutation Group which has no Finite SAGBI Bases with Respect to any Admissible Order, Theoret. Comput. Sci. 222 (1999), 177–187.
Göbel, M., Rings of Polynomial Invariants of the Alternating Group Have No Finite SAGBI Bases with Respect to any Admissible Order, Information Processing Letters. 74 (2000), 15–18.
Göbel, M., Finite SAGBI Bases for Polynomial Invariants of Conjugates of Alternating Groups, Mathematics of Computation 71 (2001), 761–765.
Göbel, M., Kredel, H., Reduction of Permutation-Invariant Polynomials. A Noncommutative Case Study, Information and Computation 175 (2002), 158–170.
Gräbe, H.-G., The Tangent Cone Algorithm and Homogeneization, J. Pure Appl. Algebra 97 (1994), 303–312.
Gräbe, H.-G., Algorithms in Local Algebra, J. Symb. Comp. 19 (1995), 545–557.
Gräbe, H.-G., Triangular Systems and Factorized Gröbner Bases, L. N. Comp. Sci. 948 (1995), 248–261, Springer.
Gräbe, H.-G., Minimal Primary Decomposition and Factoring Gröbner Bases, J. AAECC 8 (1997), 265–278.
Granger, M., Oaku, T., Takayama, N., Tangent Cone Algorithm for Homogenized Differential Operations, J. Symb. Comp. 39 (2005), 417–431.
Grassmann, H., Greuel, G.-M., Martin, B., et al., Standard Bases, Syzygies and their Implementation in SINGULAR, University of Kaiserslautern Fach. Math. Preprint 251 (1994).
Greuel, G.-M., Pfister, G., Advances and Improvements in the Theory of Standard Bases and Syzygies, Arch. Math. 66 (1996), 131–176.
Greuel, G.-M., Seelisch, F., Wienand, O., The Gröbner Basis of the Ideal of Vanishing Polynomials, J. Symb. Comp. 46 (2011), 561–570.
Gunther, N., Sur une inègalité dans la théorie des fonctions rationnelles et entieres (in Russian) [Journal de l'Institut des Ponts et Chaussées de Russie] Izdanie Inst. In?z. Putej Soob?s?cenija Imp. Al. I. 84 (1913).
Gunther, N., Sur la forme canonique des systèmes déquations homogènes (in Russian) [Journal de l'Institut des Ponts et Chaussées de Russie] Izdanie Inst. In?z. Putej Soob?s?cenija Imp. Al. I. 84 (1913).
Gunther, N., Sur les caractéristiques des systémes d’équations aux dérivées partialles, C. R. Acad. Sci. Paris 156 (1913), 1147–1150.
Gunther, N., Sur la forme canonique des equations algébriques, C. R. Acad. Sci. Paris 157 (1913), 577–80.
Gunther, N., Sur la théorie générale des systèmes d’équations aux dérivées partielles, C. R. Acad. Sci. Paris 158 (1914), 853–856, 1108–1111.
Gunther, N., Sur l'extension du théorème de Cauchy aux systèmes d’équations aux dérivées partielles (in Russian), Mat. Sbornik 32 (1924) 367–434.
Gunther, N., Sur les modules des formes algébriques, Trudy Tbilis. Mat. Inst. 9 (1941), 97–206.
Hartley, D., Tuckey, P., A Direct Characterization of Gröbner Bases in Clifford and Grassmann Algebras, J. Symb. Comp. 20 (1995), 197–205.
Hartshorne, R., Connectedness of the Hilbert Scheme, Publ. Math. I.H.E.S. 29 (1966), 261–304.
Hashemi, A., Ars, G., Extended F5 criteria, Adv. Math. 66 (1987), 171–216.
Hermiller, S. M., Kramer, X. H., Laubenbacher, R.C.Monomial Orderings, Rewriting Systems and Gröbner Bases for the Commutator Ideal of a Free Algebra, J. Symb. Comp. 27 (1999), 133–141.
Hermiller, S. M., McCammond, J., Noncommutative Gröbner Bases for the Commutator Ideal, Int. J. Algebra Comp. 16 (2006) 187–202.
Heyworth, A., One-sided Noncommutative Gröbner Bases with Applications to Computing Green's Relations, J. Algebra 242 (2001) 401–416.
Hironaka, H., Idealistic Exponents of Singularity. In: Algebraic Geometry, The Johns Hopkins Centennial Lectures (1977), 52–125.
Hulett, H., Maximum Betti Numbers of Homogeneous Ideals with a Given Hilbert Function, Communications in Algebra 21 (1993), 2335–2350.
Hulett, H., Maximum Betti Numbers for a Given Hilbert Function, PhD Thesis, Urbana- Champaign (1993).
Janet, M., Sur les systèmes d’équations aux dérivées partielles, J. Math. Pure et Appl. 3 (1920), 65–151.
Janet, M., Les modules de formes algébraiques et la théorie générale des systèmes diffèrentielles, Ann. Éc. Norm. 3e série 41 (1924), 27–65.
Janet, M., Les systèmes d’équations aux dérivées partielles, Mémorial Sci. Math. XXI (1927), Gauthiers-Villars.
Janet, M., Leçons sur les systèmes d’équations aux dérivées partielles (1929), Gauthiers-Villars.
Kandri-Rody, A., Kapur, D., Computing the Gröbner Basis of an Ideal in Polynomail Rings over the Integers. In: Proc. Third MACSYMA Users’ Conference (1984).
Kandri-Rody, A., Kapur, D., Computing the Gröbner Basis of an Ideal in Polynomail Rings over a Euclidean Ring, J. Symb. Comp. 6 (1990), 37–56.
Kandri-Rody, A., Weispfenning, W., Non-commutative Gröbner Bases in Algebras of Solvable Type, J. Symb. Comp. 9 (1990), 1–26.
Kapur, D., Madlener, K., A Completion Procedure for Computing a Canonical Basis for a k-subalgebra. In: Kaltofen, E., Watt, S. M. (Eds.), Computer and Mathematics, Springer (1989), 1–11.
Kapur, D., Sun, Y., Wang, D., A New Algorithm for Computing Comprehensive Gröbner Systems, Proc. ISSAC 2010 (2010), 29–36, ACM.
Keller, B. J., Alternatives in Implementing Noncommutative Gröbner Basis Systems, Progress in Computer Science and Applied Logic 15 (1991), 105–126, Birkhäuser.
Kobayashi, Y., A Finitely Presented Monid which has Solvable Word Problem but has no Regular Complete Presentation, Theoret. Comput. Sci. 146 (1995), 312–329.
Kredel, H., Solvable Polynomial Rings, Dissertation, Passau (1992).
Kruskal, J. B., The Theory of Well-quasi-ordering: A Frequently Discovered Concept, J. Combin. Theory Ser. A 13 (1972) 297–305.
Kühnle, K., Mayr, E.W., Exponential Space Computation of Gröbner Bases, Proc. ISSAC 96 (1996) 63–71, ACM.
Labontè, G., An Algorithm for the Construction of Matrix Representations for Finite Present Non-commutative Algebras, J. Symb. Comp. 9 (1990), 27–38.
Lambek, J., Lectures on Rings and Modules, Blaisdell (1966).
LaScala, R., Gröbner Bases and Gradings for Partial Difference Ideals, Math. Comp. 84 (2015), 959–985. arxiv.ong/pdf/1112.2065v4.pdf
LaScala, R., Levandovskyy, V., Letterplace Ideals and Non-commutative Gröbner Bases, J. Symb. Comp. 44 (2009), 1374–1393.
LaScala, R., Levandovskyy, V., Skew Polynomial Rings, Gröbner Bases and the Letterplace Embedding of the Free Associative Algebra, J. Symb. Comp. 48 (2013), 110–131.
Lascoux, A., Pragacz, P.S-function Series, J. Phys.A Math. Gen. 21 (1988), 4105– 4114.
Lauer, M., Canonical Representative for Residue Classes of a Polynomial Ideal, Proc. 1976 SymSAC, (1976) 339–345, ACM.
Lazard, D., Solving Zero-dimensional Algebraic Systems, J. Symb. Comp. 15 (1992), 117–132.
Lella, P., A Network of Rational Curves on the Hilbert Scheme, arxiv.ong/pdf/1006.5020v2.pdf
Levandovskyy, V. L., Non-commutative Computer Algebra for Polynomiakl Algebras: Gröbner Bases, Applications and ImplementationDissertation, Kaiserslautern (2005).
Levandovskyy, V. L., Studzinski, G., Schnitzler, B., Enhanced Computations of Gröbner Bases in Free Algebras as a New Application of the Letterplace ParadigmProc. ISSAC'13 (2013), 259–266, ACM.
Levin, A. B., Gröbner Bases with Respect to Several Orderings and Multivariate Dimension Polynomials, J. Symb. Comp. 42 (2007), 561–578.
Li, H., Looking for Gröbner Basis Theory for (Almost) Skew 2-nomial Algebras, J. Symb. Comp. 45 (2010), 918–942.
Liu, J., The Membership Problem for Ideals of Binomial Skew Polynomial Rings, Proc. ISSAC 2001 (2001), 192–194, ACM
Macaulay, F. S., Some Formulae in Elimination, Proc. London Math. Soc. (1) 35 (1903), 3–27.
Macaulay, F. S., The Algebraic Theory of Modular Systems, Cambridge University Press (1916).
Macaulay, F. S., Some Properties of Enumeration in the Theory of Modular Systems, Proc. London Math. Soc. 26 (1927), 531–555.
MacMillan, W. D., A Reduction of a Systems of Powers Series to an Equivalent System of Polynomials, Math. Ann. 72 (1912) 157–179.
MacMillan, W. D., A Method for Determining the Solutions of a System of Analytic Functions in the Neighborhood of a Branch Point, Math. Ann. 72 (1912), 180–202.
Madlener, K., Reinert, B., String Rewriting and Gröbner Bases – A General Approach to Monoid and Group Rings, Progr. Comp. Sci. Appl. Logic 15 (1991), 127–180, Birkhäuser.
Madlener, K., Reinert, B., Computing Gröbner Bases in Monoid and Group Rings, Proc.ISSAC '93 (1993), 254–263, ACM.
Mall, D., Characterizations of Lexicographical Sets and Simply-connected Hilbert Schemes, L. N. Comp. Sci. 1252 (1997), 221–236, Springer.
Mall, D., On the Relation between Gröbner and Pommaret Bases, J. AAECC 9 (1998), 117–124.
Mansfield, E. L., Szanto, A., Elimination Theory for Differential Difference Polynomials, Proc. ISSAC 2002 (2002), 191–198, ACM.
Månsson, J., A Prediction Algorithm for Rational Language, Licentiate Thesis, Lund University (2001).
Månsson, J., Nordbeck, B., Regular Gröbner Bases, J. Symb. Comp. 33 (2002), 163–181.
Marinari, M.G., Sugli ideali di Borel, Boll. UMI 4 (2001), 207–237.
Marinari, M.G., Ramella, L., Some Properties of Borel Ideals, J. Pure Appl. Algebra 139 (1999), 833–200.
Marinari, M.G., Ramella, L., A Characterization of Stable and Borel IdealsJ. AAECC 16 (2005), 45–68.
Marinari, M.G., Ramella, L., Borel Ideals in Three Variables, Beiträge zur Algebra und Geometrie 47 (2006), 195–209.
Markwig, T., Standard Bases in K[[t1, …, tm]][x1, …, xn]s, J. Symb. Comp. 43 (2008), 765–786.
Mårtensson, K., An Algorithm to Detect Regular Behaviour of Binomial Gröbner Basis Rational Language, Master's Thesis, Lund University (2006).
Maurer, J., Puiseux Expansions for Space Curves, Manuscripta Math., 32 (1980), 91–100.
Mayr, E.W., Ritscher, S., Dimension-dependent Bounds for Gröbner Bases of Polynomial Ideals, J. Symb. Comp. 49 (2013), 78–94.
Mayr, E.W., Ritscher, S., Space-efficient Bounds for Gröbner Bases of Polynomial Ideals, Proc. ISSAC 2011 (2011).
Maurer, J., Puiseux Expansions for Space Curves, Manuscripta Math., 32 (1980), 91–100.
Miller, J. L., Analogs of Gröbner Bases in Polynomial Rings over a Ring, J. Symb. Comp. 21 (1996), 139–153.
Miller, J. L., Effective Algorithms for Intrisic Computing SAGBI-Gröbner Base in Polynomial Rings over a Ring. In Buchberger, B., Winkler, F. (Eds.), Gröbner Bases and Application (1998) 421–433, Cambridge University Press.
Möller, H. M., On the Construction of Gröbner Bases Using Syzygies, J. Symb. Comp. 6 (1988), 345–359.
Montes, A., A New Algorithm for Discussing Gröbner Bases with Parameters, J. Symb. Comp. 33 (2002), 183–208.
Montes, A., Using Kapur–Sun–Wang Algorithm for the Gröbner Cover, Proc. EACA 2012 (2012), 135–138, Universidad de Alcalá de Henares.
Montes, A., Wibmer, M., Gröbner Bases for Polynomial Systems with Parameters, J. Symb. Comp. 45 (2010), 1391–1425.
Mosteig, E., Sweedler, M., Valuations and Filtrations, J. Symb. Comp. 34 (2002), 399–435.
Nabeshima, K., A Speed-up of the Algorithm for Computing Comprehensive Gröbner Systems, Proc. ISSAC'2007 (2007), 299–306. ACM.
Nordbeck, P., On Some Basic Applications of Gröbner Bases in Non-commutative Polynomial Rings. In: Buchberger, B., Winkler, F. (Eds.), Gröbner Bases and Application (1998) Cambridge University Press, 463–472.
Nordbeck, P., Canonical Subalgebra Bases in Non-commutative Polynomial Rings, Proc. ISSAC'98 (1998), 140–146, ACM.
Nordbeck, P., Canonical Bases for Subalgebras of Factor Algebras, Computer Science Journal of Moldavia 7 (1999), 63–79, ACM.
Norton, G. H., Sălăgean, A., Strong Gröbner Bases for Polynomials Over a Principal Ideal Ring, Bull. Austral. Math. Soc. 64 (2001), 505–528.
Norton, G. H., Sălăgean, A., Gröbner Bases and Products of Coefficient Rings, Bull. Austral. Math. Soc. 65 (2002), 147–154.
Norton, G. H., Sălăgean, A., Cyclic Codes and Minimal Strong Gröbner Bases Over a Principal Ideal Ring, Finite Fields and Their Applications 9 (2003), 237–249.
Ollivier, F., Canonical Bases: Relations with Standard Bases, Finiteness Conditions and Application to Tame Automorphisms, Progr. Math. 94 (1990), 379–400, Birkhäuser.
Ore, O., Linear Equations in Non-commutative Fields, Ann. Math. 32 (1931), 463–477.
Ore, O., Theory of Non-commutative Polynomials, Ann. Math. 34 (1933), 480–508.
Pan, L., On the D-bases of Polynomial Ideals Over Principal Ideal Domains, J. Symb. Comp. 7 (1988), 55–69.
Pauer, F., Gröbner Bases with Coefficients in Rings, J. Symb. Comp. 42 (2007), 1003–1011.
Pesch, M., Gröbner Bases in Skew Polynomial RingsDissertation, Passau (1997).
Pesch, M., Two-sided Gröbner Bases in Iterated Ore Extensions, Progr. Computer Sci. Appl. Logic 15 (1991), 225–243, Birkhäuser.
Pommaret, J. F., Systems of Partial Differential Equations and Lie Pseudogroups, Gordon and Brach (1978).
Pommaret, J. F., Haddak, A.Effective Methods for Systems of Algebraic Partial Differential Equations, Prog. Math. 94 (1990), 411–426, Birkhäuser.
Pfister, G., The Tangent Cone Algorithm and Some Applications to Local Algebraic Geometry, Progr. Math. 94 (1990), 401–410, Birkhäuser.
Pfister, G., Schönemann, H., Singularities with Exact Poincaré Complex but not Quasihomogeneous, Rev. Mat. Univ. Complutense Madrid 2 (1989), 161–174.
Pritchard, F. L., A Syzygies Approach to Non-commutative Gröbner Bases, Preprint (1994).
Pritchard, F. L., The Ideal Membership Problem in Non-commutative Polynomial Rings, J. Symb. Comp. 22 (1996), 27–48.
Rajee, S., Non-associative Gröbner Bases, J. Symb. Comp. v (2006), 887–904.
Renschuch, B., Roloff, H., Rasputin, G. G. et. al., Beiträge zur konstructiven Theorie des Polynomideal XXIII: Vergessene Arbeiten des Leningrader Mathematikers N.M. Gjunter on Polynomial Ideals, Wiss. Z. Pädagogische Hochschule Karl Liebknecht, Postdam, 31 (1987) 111–126. English translation (by M. Abramson) in ACM SIGSAM Bull. 37 (2003) 35–48.
Reichstein, Z., SAGBI Bases in Rings of Multiplicative Invariants, Comment. Math. Helv. 78, 185–202.
Reinert, B., On Gröbner Basis in Monoids and Group Rings, Dissertation, Kaiserslautern (1995).
Reinert, B., A Systematic Study of Gröbner Basis Methods, Habilitation, Kaiserslautern (2003).
Reinert, B., Gröbner Bases in Function Ring – A Guide for Introducing Reduction Relations to Algebraic Structures, J. Symb. Comp. 41 (2006), 1264–1294.
Richman, F., Constructive Aspects of Noetherian Rings, Proc. AMS 44 (1974), 436–441.
Riquier, C., De l'existence des intégrales dans un système differentiel quelconque, Ann. Éc. Norm. 3e série 10 (1893) 65–86.
Riquier, C., Sur une questione fondamentale du Calcul intégral, Acta Mathematica 23 (1899), 203.
Riquier, C., Les systèmes d’équations aux dérivées partielles (1910), Gauthiers-Villars.
Riordan, J., Combinatorial Identities (1968), Wiley.
Ritt, J. F., Prime and Composite Polynomials. Trans. A.M.S. 23 (1922), 51–66.
Ritt, J. F., Differential Equations from the Algebraic Standpoint, A.M.S. Colloquium Publications 14 (1932).
Ritt, J. F., Differential Algebra, A.M.S. Colloquium Publications 33 (1950).
Robbiano, L., Sweedler, M., Subalgebra Bases, L. Math. 1430 (1988), 61–87, Springer.
Robinson, L. B., Sur les systémes d’équations aux dérivées partialles, C. R. Acad. Sci. Paris 157 (1913), 106–108.
Robinson, L. B.A new Canonical Form for Systems of Partial Differential Equations, Amer. J. Math. 39 (1917), 95–112.
Rosenmann, A., An Algorithm for Constructing Gröbner and Free Schreier Bases in Free Group Algebras, J. Symb. Comp. 16 (1993), 523–549.
Saito, T., Iwamoto, T., Kobayasli, Y., Kajitori, K., Strongly Compatible Total Orders on Free Monoids, Semigroup Forum 43 (1991), 357–366.
Saito, T., Katsura, M., Kobayasli, Y., Kajitori, K., On Totally Ordered Free Monoids. In: Words, Language and Combinatorics, World Scientific (1992), 454–479.
Salomaa, A., Jewels of Formal Language Theory, Pitmann (1981).
Saracino, D., Weispfenning, V., On Algebraic Curves Over Commutative Regular Rings, L. Math. 498 (1975), 307–383, Springer.
Sato, Y., Suzuki, A., Discrete Comprehensive Gröbner Bases, Proc. ISSAC 2001 (2001), 292– 296, ACM.
Sato, Y., Suzuki, A., An Alternative Approach to Comprehensive Gröbner Bases, J. Symb. Comp. 36 (2003), 649–667.
Sato, Y., Suzuki, A., A Simple Algorithm to Compute Comprehensive Gröbner Bases, Proc. ISSAC 2006 (2006), 326–331, ACM.
Schaller, S. C., Algorithmic Aspects of Polynomial Residue Class Rings, Thesis, University of Wisconsin at Madison (1975).
Schwartz, F., The Riquier–Janet Theory and its Applications to Nonlinear Evolution Equations, Physica 11D (1984), 243–251.
Schwartz, F., Reduction and Completion Algorithm for Partial Differential Equations, Proc. ISSA'92 (1992), 49–56, ACM.
Schwartz, F., Janet Bases for Symmetry Groups In: Buchberger, B., Winkler, F. (Eds.), Gröbner Bases and Application (1998), 221–234.
Shirayanagi, K., A Classification of Finite-dimensional Monomial AlgebrasProgr. Math. 94 (1990), 469–482, Birkhäuser.
Shirayanagi, K., Decision of Algebra Isomorphisms Using Gröbner Bases, Progr. Math. 109 (1993), 253–266, Birkhäuser.
Sit, W.Y., A Theory for Parametric Linear Systems, Proc. ISSAC'91 (1991), 112–121, ACM.
Sperner, E., Über einen kombinatorishen Satz von Macaulay und seine Anwerdungen auf die Theorie der Polynomideale, Abh. Math. Sem. Univ. Hamburg 7 (1930), 149–163.
Squier, C.C., Word Problems and a Homological Finiteness Condition for Monoids, J. Pure Appl. Algebra 49 (1987), 201–217.
Stillman, M., Tsai, H., Using SAGBA Bases for Computing Invariants, J. Pure Appl. Algebra 139 (1999), 285–302.
Szekeres, L., A Canonical Basis for the Ideals of a Polynomial Domain, Am. Math. Monthly 59 (1952), 379–386.
Sweedle, M., Ideal Bases and Valuation Rings, Manuscript (1986) available at http://math.usask.ca/fvk/Valth.html
Tamari, D., On a Certain Classification of Rings and Semigroups, Bull. A.M.S. 54 (1948), 153–158.
Thierry, N.M., Thomassé, S., Convex Cones and SAGBI Bases of Permutation Invariants. In: Invariant Theory in all Characteristics, CRM Proc. Lecture Notes, 35 (2004), 259–263, AMS.
Torstensson, A., Using Resultnats for SAGBI Basis Verification in the Univariate Polynomial Ring, J. Symb. Comp. 40 (2002), 1087–1105.
Torstensson, A., Ufnarovski, V., Öfverbeck, H., Canonical Bases for Subalgebras on Two Generators in the Univariate Polynomial Ring, Beiträge Algebra Geom. 43 (2005), 565–577.
Ufnarovski, V., A Growth Criterion for Graphs and Algebras Defined by Words, Math. Notes 31 (1983), 238–241.
Ufnarovski, V., On the use of Graphs for Computing a Basis, Growth and Hilbert Series of Associative Algebras, Math. Sb. 180 (1989), 1548–1560.
Ufnarovski, V., Combinatorial and Asymptotic Methods in Algebra. In: Kostrikin, A. I., Shafarevich, I. R. (Eds.), Algebra-VI (1995), Springer, 5–196.
Ufnarovski, V., Introduction to Noncommutative Gröbner Bases Theory. In: Buchberger, B., Winkler, F. (Eds.), Gröbner Bases and Application (1998), Cambridge University Press, 259–280.
Weispfenning, V., Gröbner Bases for Polynomial Ideals over Commutative Regular Rings, L. N. Comp. Sci. 378 (1987), 336–347, Springer.
Weispfenning, V., Comprehensive Gröbner Bases, J. Symb. Comp. 14 (1992), 1–29.
Weispfenning, V.Finite Gröbner Bases in Non-Noetherian Skew Polynomial Rings, Proc. ISSAC'92 (1992), 320–332, ACM.
Weispfenning, V., Canonical Comprehensive Gröbner Bases, J. Symb. Comp. 36 (2003), 669–683.
Weispfenning, V., Comprehensive Gröbner Bases and Regular Rings, J. Symb. Comp. 41 (2006), 285–296.
Wibmer, M.Gröbner Bases for Families of Affine or Projective Schemes, J. Symb. Comp. 42 (2007), 803–834.
Wiesinger-Widi, M.Gröbner Bases and Generalized Sylvester Matrices. PhD Thesis, Johannes Kepler University, Institute for Symbolic Computation, submitted 2014.
Zariski, O., Samuel, P., Commutative Algebra, Van Nostrand (1958).
Zacharias, G., Generalized Gröbner Bases in Commutative Polynomial Rings, Bachelor's Thesis, MIT (1978).
Zarkov, A., Solving Zero-dimensional Involutive Systems, Progr. Math. 143 (1996), 389–399, Birkhäuser.
Zarkov, A., Blinkov, Y., Involution Approach to Investing Polynomial Systems, Math. Comp. Simul. 42 (1996), 323–332.