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(STRONGLY) GORENSTEIN FLAT MODULES OVER GROUP RINGS

Part of: Modules, bimodules and ideals Rings and algebras arising under various constructions Connections with homological algebra and category theory

Published online by Cambridge University Press:  17 December 2013

ABDOLNASER BAHLEKEH
ABDOLNASER BAHLEKEH*
Affiliation:
Department of Mathematics, Gonbade-Kavous University, 4971799151 Gonbade-Kavous, Iran email [email protected] School of Mathematics, Institute for Research in Fundamental Science (IPM), PO Box 19395-5746, Tehran, Iran email [email protected]
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Abstract

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Let $\Gamma $ be a group and ${\Gamma }^{\prime } $ be a subgroup of $\Gamma $ of finite index. Let $M$ be a $\Gamma $-module. It is shown that $M$ is (strongly) Gorenstein flat if and only if it is (strongly) Gorenstein flat as a ${\Gamma }^{\prime } $-module. We also provide some criteria in which the classes of Gorenstein projective and strongly Gorenstein flat $\Gamma $-modules are the same.

Keywords

Gorenstein flat modulestrongly Gorensein flat moduleGorenstein projective modulegroup ring

MSC classification

Secondary: 20J05: Homological methods in group theory 16D40: Free, projective, and flat modules and ideals 16S34: Group rings , Laurent polynomial rings
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 90 , Issue 1 , August 2014 , pp. 57 - 64
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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