On modules M such that M and M* are semi-Gorenstein-projective

2020/05/18 by Ringel, Claus Michael, Zhang, Pu
#Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2005.08779

Abstract

Let A be an artin algebra. An A-module M is semi-Gorenstein-projective provided that Extⁱ(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.

Related

• Thick subcategories and virtually Gorenstein algebras
• Gorenstein-projective and semi-Gorenstein-projective modules. II
• Gorenstein Homological Algebra of Artin Algebras
• k-Gorenstein Modules
• Strongly Gorenstein projective, injective, and flat modules