Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-25T06:56:17.802Z Has data issue: false hasContentIssue false
  • English
  • Français

Semigroup-graded rings with finite support

Published online by Cambridge University Press:  18 May 2009

M. V. Clase ,
E. Jespers  and
A. Del Río
M. V. Clase
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, OntarioCanada L8S 4K1
E. Jespers
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. Johns, Newfoundland, Canada A1C 5S7
A. Del Río
Affiliation:
Departamento de Matemáticas, Universidad de Murcia, 30071 Murcia, Spain
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let S be a semigroup and let be an S-graded ring. Rs = 0 for all but finitely many elements s ∈ S1, then R is said to have finite support. In this paper we concern ourselves with the question of whether a graded ring R with finite support inherits a given ring theoretic property from the homogeneous subrings Re corresponding to idempotent semigroup elements e.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 38 , Issue 1 , January 1996 , pp. 11 - 18
Copyright
Copyright © Glasgow Mathematical Journal Trust 1996

References

REFERENCES

1.Beattie, M. and Jespers, E., On perfect graded rings, Comm. Algebra 19 (1991), 2363–2371.CrossRefGoogle Scholar
2.Clase, M. V., Semigroup graded rings, Ph.D. thesis, Memorial University of Newfoundland (1993).Google Scholar
3.Clase, M. V. and Jespers, E., Perfectness of rings graded by finite semigroups, Bull. Soc.Math. Bel. Sir. A 45 (1993), 93–102.Google Scholar
4.Clase, M. V. and Jespers, E., On the Jacobson radical of semigroup graded rings, J. Algebra 169 (1994), 79–97.CrossRefGoogle Scholar
5.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, two volumes (American Mathematical Society, 1961).Google Scholar
6.Cohen, M. and Rowen, L. H., Group graded rings, Comm. Algebra 11 (1983), 1253–1270.CrossRefGoogle Scholar
7.Dăscălescu, S., Năstăsescu, C., Rio, A. del, and Oystaeyen, F. Van, Gradings of finite support. Applications to injective objects, J. Pure Appl. Algebra, to appear.Google Scholar
8.Higman, G., Finitely presented infinite simple groups, Notes on Pure Mathematics, vol. 8, I.A. S. Australian National University, (1974).Google Scholar
9.Jaegermann, M. and Sands, A. D., On normal radicals, N-radicals, and A-radicals, J.Algebra 5O (1978), 337–349.CrossRefGoogle Scholar
10.Jespers, E. and Oknińnski, J., Descending chain conditions and graded rings, J. Algebra, to appear.Google Scholar
11.Kelarev, A. V., On semigroup graded PI-algebras, Semigroup Forum 47 (1993), 294–298.CrossRefGoogle Scholar
12.Menini, C., Finitely graded rings, Morita duality and self-injectivity, Comm. Algebra 15 (1987), 1779–1797.CrossRefGoogle Scholar
13.Menini, C. and Năastăasescu, C., gr-simple modules and gr-Jacobson radical. Applications, Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 34 (82) (1990), 25–36.Google Scholar
14.Menini, C. and Năastăasescu, C., gr-simple modules and gr-Jacobson radical. Applications II, Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 34 (82) (1990), 125–133.Google Scholar
15.Năstăsescu, C., Some constructions over graded rings: applications, J. Algebra 120 (1989), 119–138.CrossRefGoogle Scholar
16.Passman, D. S., Infinite crossed products (Academic Press, 1989).Google Scholar
17.Rowen, L. H., General polynomial identities. II, J. Algebra 38 (1976), 380–392.CrossRefGoogle Scholar
18.Watters, J. F., Polynomial extensions of Jacobson rings, J. Algebra 36 (1975), 302–308.CrossRefGoogle Scholar