Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T14:04:21.152Z Has data issue: false hasContentIssue false
  • English
  • Français

A commutative Noetherian ring which possesses a dualizing complex is acceptable

Published online by Cambridge University Press:  24 October 2008

Rodney Y. Sharp
Rodney Y. Sharp
Affiliation:
University of Sheffield
Get access Rights & Permissions [Opens in a new window]

Extract

Throughout this paper the word ‘ring’ will mean ‘commutative Noetherian ring with non-zero identity’, and A will always denote such a ring. It will only be assumed that A is local when this is explicitly stated, but when this is the case m (resp. k) will always be used to denote the maximal ideal (resp. residue field) of A. It is to be understood that ring homomorphisms respect identity elements.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 82 , Issue 2 , September 1977 , pp. 197 - 213
Copyright
Copyright © Cambridge Philosophical Society 1977

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Bass, H.On the ubiquity of Gorenstein rings. Math. Z. 82 (1963), 8–28.Google Scholar
(2)Beck, I.Σ-injective modules. J. Algebra 21 (1972), 232–249.Google Scholar
(3)Cartan, H. and Eilenberg, S.Homological algebra (Princeton University Press, 1956).Google Scholar
(4)Douglas, A. J.An elementary derivation of certain homological inequalities. Mathematika 10 (1963), 114–124.CrossRefGoogle Scholar
(5)Fossum, R., Foxby, H.-B., Griffith, Ph. and Reiten, I.Minimal injective resolutions with applications to dualizing modules and Gorenstein modules. Inst. Hautes Études Sci. Publ. Math. 45 (1975), 193–215.CrossRefGoogle Scholar
(6)Hartshorne, R.Residues and duality (Springer Lecture Notes in Mathematics, no. 20, 1966).CrossRefGoogle Scholar
(7)Levin, G. and Vasconcelos, W. V.Homological dimensions and Macaulay rings. Pacific J. Math. 25 (1968), 315–323.Google Scholar
(8)Matsumura, H.Commutative algebra (Benjamin, 1970).Google Scholar
(9)Northcott, D. G.An introduction to homological algebra (Cambridge University Press, 1960).CrossRefGoogle Scholar
(10)Northcott, D. G.Lessons on rings, modules and multiplicities (Cambridge University Press, 1968).CrossRefGoogle Scholar
(11)Reiten, I.The converse to a theorem of Sharp on Gorenstein modules. Proc. Amer. Math. Soc. 32 (1972), 417–420.Google Scholar
(12)Sharp, R. Y.The Cousin complex for a module over a commutative Noetherian ring. Math. Z. 112 (1969), 340–356.Google Scholar
(13)Sharp, R. Y.Gorenstein modules. Math. Z. 115 (1970), 117–139.Google Scholar
(14)Sharp, R. Y.Local cohomology theory in commutative algebra. Quart. J. Math. Oxford 21 (1970), 425–434.Google Scholar
(15)Sharp, R. Y.On Gorenstein modules over a complete Cohen–Macaulay local ring. Quart. J. Math. Oxford 22 (1971), 425–434.Google Scholar
(16)Sharp, R. Y.Finitely generated modules of finite injective dimension over certain Cohen–Macaulay rings. Proc. London Math. Soc. 25 (1972), 303–328.Google Scholar
(17)Sharp, R. Y.The Euler characteristic of a finitely generated module of finite injective dimension. Math. Z. 130 (1973), 79–93.CrossRefGoogle Scholar
(18)Sharp, R. Y.Dualizing complexes for commutative Noetherian rings. Math. Proc. Cambridge Philos. Soc. 78 (1975), 369–386.Google Scholar
(19)Sharp, R. Y.Acceptable rings and homomorphie images of Gorenstein rings. J. Algebra 44 (1977), 246–261.Google Scholar
(20)Sharpe, D. W. and Vámos, P.Injective modules (Cambridge University Press, 1972).Google Scholar