Cohomology theories based on Gorenstein injective modules
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- by Javad Asadollahi and Shokrollah Salarian PDF
- Trans. Amer. Math. Soc. 358 (2006), 2183-2203 Request permission
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.References
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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
- MR Author ID: 55173
- ORCID: 0000-0002-7330-2558
- 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
- Received by editor(s): April 23, 2003
- Received by editor(s) in revised form: June 15, 2004
- Published electronically: August 1, 2005
- Additional Notes: This research was supported in part by a grant from IPM (No. 82130113 and No. 82130118)
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 358 (2006), 2183-2203
- MSC (2000): Primary 13D05, 13D45, 13H10, 13D03, 55N35
- DOI: https://doi.org/10.1090/S0002-9947-05-03749-9
- MathSciNet review: 2197453