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An infinite construction in ring theory

Published online by Cambridge University Press:  18 May 2009

E. A. Whelan
E. A. Whelan
Affiliation:
School of Mathematics and Physics, University of East Anglia, Norwich, Norfolk NR4 7TJ, England
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In this note we describe a class of functors on the category of associative rings with unity (hereafter “rings”) and of ring homomorphisms which, loosely speaking, ‘preserve the properties’ of two-sided ideals, but can be chosen to be arbitrarily ‘bad’ for one-sided properties of rings.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 3 , September 1988 , pp. 349 - 357
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

References

1.Azumaya, G., Separable rings, J. Algebra 63 (1980), 1–14.CrossRefGoogle Scholar
2.Chatters, A. W., Non-commutative unique factorization domains, Math. Proc. Camb. Phil. Soc., 95 (1984), 49–54.CrossRefGoogle Scholar
3.Chatters, A. W. and Jordan, D. A., Non-commutative unique factorisation rings, J. London Math. Soc. (2) 33 (1986), 22–32.CrossRefGoogle Scholar
4.Demeyer, F. and Ingraham, E., Separable algebras over commutative rings, Lecture Notes in Mathematics No. 181Springer-Verlag, 1971).CrossRefGoogle Scholar
5.Gilchrist, M. P. and Smith, M. K., Noncommutative UFD's are often PID's Math. Proc. Camb. Phil. Soc., 95 (1984), 417–419.CrossRefGoogle Scholar
6.Jategaonkar, A. V., Noetherian bimodules, primary decomposition and Jacobson's conjecture, Algebra 71 (1981), 379–400.CrossRefGoogle Scholar
7.Jategaonkar, A. V., Left principal ideal rings, Lecture Notes in Mathematics No. 123 (Springer-Verlag, 1970).CrossRefGoogle Scholar
8.Jategaonkar, A. V., Localization in noetherian rings, London Math. Soc. Lecture Notes Series No. 98, (Cambridge University Press, 1986).CrossRefGoogle Scholar
9.Le Bruyn, L., Trace rings of generic matrices are unique factorisation domains, Glasgow Math. J. 28 (1986), 11–13.CrossRefGoogle Scholar
10.Nagata, M., Local rings. (Interscience, New York, 1962).Google Scholar
11.Robson, J. C., On PRI and IPRI rings, Quart. J. Math. Oxford (2), 18 (1967), 125–145.CrossRefGoogle Scholar
12.Robson, J. C., Idealizers and hereditary noetherian prime rings, J. Algebra 22 (1972), 45–81.CrossRefGoogle Scholar
13.Sugano, K., Note on cyclic Galois extensions, Proc. Japan Acad., 57 Ser. A (1981), 60–63.Google Scholar
14.Whelan, E. A., Reduced rank and normalising elements. J. Algebra 113 (1988), 416–429.CrossRefGoogle Scholar
15.Whelan, E. A., Thesis (University of East Anglia, 1986).Google Scholar
16.Whelan, E. A., Normalising elements and radicals. Bull. Austral. Math. Soc. Ser. A., to appear.Google Scholar
17.Whelan, E. A., Quasi-commutative principal ideal rings. Quart. J. Math. Oxford (2) 37 (1986), 375–383.CrossRefGoogle Scholar
18.Whelan, E. A., Not-necessarily commutative unique factorisation rings, to be submitted to Quart. J. Math. Oxford (2).Google Scholar
19.Whelan, E. A., Radical properties and the Jacobson conjecture, in preparation.Google Scholar