Gorenstein injective modules and local cohomology

Author:

Sazeedeh Reza

Abstract

In this paper we assume that R R is a Gorenstein Noetherian ring. We show that if ( R , m ) (R,\mathfrak {m}) is also a local ring with Krull dimension d d that is less than or equal to 2, then for any nonzero ideal a \mathfrak {a} of R R , H a d ( R ) H_{\mathfrak {a}}^d(R) is Gorenstein injective. We establish a relation between Gorenstein injective modules and local cohomology. In fact, we will show that if R R is a Gorenstein ring, then for any R R -module M M its local cohomology modules can be calculated by means of a resolution of M M by Gorenstein injective modules. Also we prove that if R R is d d -Gorenstein, M M is a Gorenstein injective and a \mathfrak a is a nonzero ideal of R R , then Γ a ( M ) {\Gamma }_{\mathfrak {a}}(M) is Gorenstein injective.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

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