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Cohomology theories based on Gorenstein injective modules

Author(s): Javad Asadollahi; Shokrollah Salarian
Journal: Trans. Amer. Math. Soc. 358 (2006), 2183-2203.
MSC (2000): Primary 13D05, 13D45, 13H10, 13D03, 55N35
Posted: August 1, 2005
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Abstract: In this paper we study relative and Tate cohomology of modules of finite Gorenstein injective dimension. Using these cohomology theories, we present variations of Grothendieck local cohomology modules, namely Gorenstein and Tate local cohomology modules. By applying a sort of Avramov-Martsinkovsky exact sequence, we show that these two variations of local cohomology are tightly connected to the generalized local cohomology modules introduced by J. Herzog. We discuss some properties of these modules and give some results concerning their vanishing and non-vanishing.

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Additional Information:

Javad Asadollahi
Affiliation: School of Mathematics, Institute for Studies in Theoretical Physics and Mathematics (IPM), P.O. Box 19395-5746, Tehran, Iran -- and -- Shahre-Kord University, P.O. Box 115, Shahre-Kord, Iran
Email: Asadollahi@ipm.ir

Shokrollah Salarian
Affiliation: School of Mathematics, Institute for Studies in Theoretical Physics and Mathematics (IPM), P.O. Box 19395-5746, Tehran, Iran -- and -- Department of Mathematics, University of Isfahan, P.O. Box 81746-73441, Isfahan, Iran
Email: Salarian@ipm.ir

DOI: 10.1090/S0002-9947-05-03749-9
PII: S 0002-9947(05)03749-9
Keywords: Gorenstein injective coresolutions, local cohomology modules, Tate cohomology, Gorenstein rings, Gorenstein dimension
Received by editor(s): April 23, 2003
Received by editor(s) in revised form: June 15, 2004
Posted: August 1, 2005
Additional Notes: This research was supported in part by a grant from IPM (No. 82130113 and No. 82130118)
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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