On modules M such that M and M* are semi-Gorenstein-projective
Claus Michael Ringel, Pu Zhang
TL;DR
This paper investigates modules over artin algebras where both the module and its dual are semi-Gorenstein-projective, providing detailed analysis and clarifying their properties beyond Gorenstein-projective modules.
Contribution
It offers a detailed analysis of modules with semi-Gorenstein-projective modules and their duals, extending understanding beyond Gorenstein-projective modules.
Findings
Modules with both M and M* semi-Gorenstein-projective are characterized.
The converse of Gorenstein-projectivity implying semi-Gorenstein-projectivity is shown not to hold.
The paper clarifies properties of modules where both M and M* are semi-Gorenstein-projective.
Abstract
Let A be an artin algebra. An A-module M is semi-Gorenstein-projective provided that Ext^i(M,A) = 0 for all i > 0. If M is Gorenstein-projective, then both M and its A-dual M* are semi-Gorenstein projective. As we have shown recently, the converse is not true, thus answering a question raised by Avramov and Martsinkovsky. The aim of the present note is to analyse in detail the modules M such that both M and M* are semi-Gorenstein-projective.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Commutative Algebra and Its Applications