Gorenstein injective modules and local cohomology

Author:
Reza Sazeedeh

Journal:
Proc. Amer. Math. Soc. **132** (2004), 2885-2891

MSC (2000):
Primary 13D05, 13D45

DOI:
https://doi.org/10.1090/S0002-9939-04-07461-1

Published electronically:
May 21, 2004

MathSciNet review:
2063107

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Abstract: In this paper we assume that is a Gorenstein Noetherian ring. We show that if is also a local ring with Krull dimension that is less than or equal to 2, then for any nonzero ideal of , 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 is a nonzero ideal of , then is Gorenstein injective.

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Additional Information

**Reza Sazeedeh**

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

DOI:
https://doi.org/10.1090/S0002-9939-04-07461-1

Keywords:
Cover,
Gorenstein injective,
Gorenstein projective,
local cohomology

Received by editor(s):
December 5, 2002

Received by editor(s) in revised form:
June 21, 2003

Published electronically:
May 21, 2004

Communicated by:
Bernd Ulrich

Article copyright:
© Copyright 2004
American Mathematical Society