A functorial approach to modules of G-dimension zero

2004/08/12 by Yuji Yoshino, Yoshino, Yuji · 1 citation
Mathematics · #13C #13D #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA) #math.AC #math.RA #msc:13C #msc:13D

paper · pdf · doi:10.48550/arxiv.math/0408162

22 pages

arxiv created 2004/08/12 · arxiv updated 2009/12/01

Abstract

Let R be a commutative Noetherian ring and let \G be the category of modules of G-dimension zero over R. We denote the associated stable category by \pG. We show that the functor category \modpG is a Frobenius category and we argue how this property could characterize \G as a subcategory of \modR.

Cited by

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

Related

• The stable module category of a general ring
• The monomorphism category of Gorenstein projective modules and comparision with the category of matrix factorization
• Modules of G-dimension zero over local rings with the cube of maximal ideal being zero
• The Acyclicity of the Frobenius Functor for Modules of Finite Flat Dimension
• The dimension of a subcategory of modules