The converse to a theorem of Sharp on Gorenstein modules

Reiten, Idun

doi:10.1090/S0002-9939-1972-0296067-7

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
DOI: https://doi.org/10.1090/S0002-9939-1972-0296067-7
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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