Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-01-27T12:42:06.387Z Has data issue: false hasContentIssue false
  • English
  • Français

Injective homogeneity and the Auslander–Gorenstein property

Published online by Cambridge University Press:  18 May 2009

Zhong Yi
Zhong Yi
Affiliation:
Department of Mathematics, University of Glasgow, University Gardens, Glasgow, G12 8QW, Scotland, U.K.
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.

In this paper we refer to [13] and [16] for the basic terminology and properties of Noetherian rings. For example, an FBNring means a fully bounded Noetherian ring [13, p. 132], and a cliqueof a Noetherian ring Rmeans a connected component of the graph of links of R[13, p. 178]. For a ring Rand a right or left R–module Mwe use pr.dim.(M) and inj.dim.(M) to denote its projective dimension and injective dimension respectively. The right global dimension of Ris denoted by r.gl.dim.(R).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 37 , Issue 2 , May 1995 , pp. 191 - 204
Copyright
Copyright © Glasgow Mathematical Journal Trust 1995

References

REFERENCES

1.Anderson, F. W. and Fuller, K. R., Rings and categories of modules (Springer, 1974).CrossRefGoogle Scholar
2.Bass, H., On the ubiquity of Gorenstein rings, Math. Z. 82 (1963), 8–28.CrossRefGoogle Scholar
3.Bell, A. D., Notes on localization in noncommutative Noetherian rings, Cuadernos De Algebra 9, Universidad de Granada (1988).Google Scholar
4.Björk, J.–E., The Auslander condition on noetherian rings, Séminaire d'Algèbre P. Dubreil et M. P.Malliavin 1987–1988, Lecture Notes in Mathematics 1404 (Springer, 1989), 137–173.Google Scholar
5.Brown, K. A., Localization at cliques in group rings, J. Pure Appl. Algebra 41 (1986), 9–16.CrossRefGoogle Scholar
6.Brown, K. A. and Hajarnavis, C. R., Homologically homogeneous rings, Trans. Amer. Math. Soc. 281 (1984), 197–208.CrossRefGoogle Scholar
7.Brown, K. A. and Hajarnavis, C. R., Injectively homogeneous rings, J. Pure Appl. Algebra 51 (1988), 65–77.CrossRefGoogle Scholar
8.Brown, K. A. and Levasseur, T., Cohomology of bimodules over enveloping algebras, Math. Z. 189 (1985), 393–413.CrossRefGoogle Scholar
9.Cohen, M. and Montgomery, S., Group–graded rings, smash products, and group actions, Trans. Amer. Math. Soc. 282 (1984), 237–258.CrossRefGoogle Scholar
10.Dade, E. C., Group–graded rings and modules, Math. Z. 174 (1980), 241–262.CrossRefGoogle Scholar
11.Goodearl, K. R. and Jordan, D. A., Localizations of injective modules, Proc. Edinburgh Math. Soc. 28 (1985), 289–299.CrossRefGoogle Scholar
12.Goodearl, K. R. and Small, L. W., Krull versus global dimension in Noetherian P.I. rings, Proc. Amer. Math. Soc. 92 (1984), 175–178.CrossRefGoogle Scholar
13.Goodearl, K. R. and JrWarfield, R. B., An introduction to noncommutative Noetherian rings (Cambridge University Press, 1989).Google Scholar
14.Letzter, E. S., Prime ideals in finite extensions of Noetherian rings, J. Algebra 135 (1990), 412–439.CrossRefGoogle Scholar
15.Levasseur, T., Some properties of noncommutative regular graded rings, Glasgow Math. J. 34 (1992), 277–300.CrossRefGoogle Scholar
16.McConnell, J. C. and Robson, J. C., Noncommutative Noetherian rings (Wiley–Interscience, 1987).Google Scholar
17.Montgomery, S., Fixed rings of finite automorphism groups of associative rings, Lecture Notes in Mathematics 818 (Springer, 1980).CrossRefGoogle Scholar
18.Năstăsescu, C., Strongly graded rings of finite groups, Comm. Algebra 11 (1983), 1033–1071.CrossRefGoogle Scholar
19.Năstăsescu, C. and Oystaeyen, F. Van, Graded ring theory (North Holland, 1982).Google Scholar
20.Northcott, D. G., An introduction to homological algebra (Cambridge University Press, 1960).CrossRefGoogle Scholar
21.Passman, D. S., Infinite crossed products (Academic Press, 1989).Google Scholar
22.Quinn, D., Group–graded rings and duality, Trans. Amer. Math. Soc. 292 (1985), 155–167.CrossRefGoogle Scholar
23.Rotman, J. J., An introduction to homological algebra (Academic Press, 1979).Google Scholar
24.Stafford, J. T., Infinite cliques in Noetherian rings, preprint, University of Michigan.Google Scholar
25.Stafford, J. T. and Zhang, J. J., Homological properties of (graded) Noetherian P.I. rings, J. Algebra 168 (1994), 988–1026.CrossRefGoogle Scholar
26.Stenstrom, B., Rings of quotients (Springer, 1975).CrossRefGoogle Scholar
27.JrWarfield, R. B., Noncommutative localized rings, Séminaire d'Algèbre P. Dubreil et M. P. Mallavin 1985, Lecture Notes in Mathematics 1220 (Springer, 1986), 178–200.Google Scholar
28.Yi, Z., Homological dimension of skew group rings and crossed products, J. Algebra 164 (1994), 101–123.CrossRefGoogle Scholar
29.Zaks, A., Injective dimension of semi–primary rings, J. Algebra, 13 (1969), 73–86.CrossRefGoogle Scholar