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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The converse to a theorem of Sharp on Gorenstein modules


Author: Idun Reiten
Journal: Proc. Amer. Math. Soc. 32 (1972), 417-420
MSC: Primary 13H10
MathSciNet review: 0296067
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Abstract: Let A be a commutative local Noetherian ring with identity of Krull dimension n, m its maximal ideal. Sharp has proved that if A is Cohen-Macauley and a homomorphic image of a Gorenstein local ring, then A has a Gorenstein module M with $ {\dim _{A/m}}\operatorname{Ext}^n(A/m,M) = 1$. The aim of this note is to prove the converse to this theorem.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0296067-7
PII: S 0002-9939(1972)0296067-7
Keywords: Commutative Noetherian ring, Cohen-Macaulay ring, Gorenstein ring, Gorenstein module
Article copyright: © Copyright 1972 American Mathematical Society