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Gorenstein injective modules and local cohomology

Authors:	Reza Sazeedeh

Institution:	Institute of Mathematics, University for Teacher Education, 599, Taleghani Avenue, Tehran 15614, Iran -- and -- Department of Mathematics, Urmia University, Iran

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

Keywords:	Cover Gorenstein injective Gorenstein projective local cohomology

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