Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Cohomology theories based on Gorenstein injective modules


Authors: Javad Asadollahi and Shokrollah Salarian
Journal: Trans. Amer. Math. Soc. 358 (2006), 2183-2203
MSC (2000): Primary 13D05, 13D45, 13H10, 13D03, 55N35
Published electronically: August 1, 2005
MathSciNet review: 2197453
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 13D05, 13D45, 13H10, 13D03, 55N35

Retrieve articles in all journals with MSC (2000): 13D05, 13D45, 13H10, 13D03, 55N35


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: http://dx.doi.org/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
Published electronically: August 1, 2005
Additional Notes: This research was supported in part by a grant from IPM (No. 82130113 and No. 82130118)
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.