Abstract.
Let \((R, \frak {m})\) be a commutative Gorenstein complete local ring with dim R = d and let \(\Lambda \) be an R-algebra which is not necessarily commutative but finitely generated as an R-module. In this paper the structure of minimal injective resolutions \(E^\bullet _\Lambda (M)\) for the \(\Lambda \)-lattices M is explored, in terms of the Cousin complexes \(C^{\bullet }_R(M)\) for M and the minimal projective resolutions of the \(\Lambda ^{op}\)-modules \(M^* = \hbox {Hom}_R(M,R)\) as well, under the assumption that \(\Lambda \) is a Cohen-Macaulay isolated singularity. As a consequence we get the following. Assume that R is a regular local ring and let \(k \in \Bbb Z\). Then the ring \(\Lambda \) is k-Gorenstein if and only if the ring \(\Delta = (R/\frak {m})\otimes _R \Lambda \) is (k - d)-Gorenstein.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 15.6.1998
Rights and permissions
About this article
Cite this article
Goto, S., Nishida, K. Minimal injective resolutions of Cohen-Macaulay isolated singularities. Arch. Math. 73, 249–255 (1999). https://doi.org/10.1007/s000130050394
Issue Date:
DOI: https://doi.org/10.1007/s000130050394