Gorenstein-projective and semi-Gorenstein-projective modules. II

2019/05/10 by Claus Michael Ringel, Pu Zhang, Ringel, Claus Michael +1 · 1 citation
Mathematics · #16E05 #16E65 #16G10 #16G50 (Primary) #20G42 (Secondary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1905.04048

openalex publication_date 2019/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be a field and q a non-zero element of k. In Part I, we have exhibited a 6-dimensional k-algebra A = A(q) and we have shown that if q has infinite multiplicative order, then A has a 3-dimensional local module which is semi-Gorenstein-projective, but not torsionless, thus not Gorenstein-projective. This Part II is devoted to a detailed study of all the 3-dimensional local A-modules for this particular algebra A. If q has infinite multiplicative order, we will encounter a whole family of 3-dimensional local modules which are semi-Gorenstein-projective, but not torsionless.

Cited by

• Claus Michael Ringel's main contributions to Gorenstein-projective modules

Related

• Gorenstein-projective modules over short local algebras
• On modules M such that M and M* are semi-Gorenstein-projective
• On stable modules that are not Gorenstein projective
• A description of Gorenstein projective modules over the tensor products of algebras
• When every Gorenstein projective (resp. flat) module is strongly Gorenstein projective (resp. flat)