On the Subcategories of n-Torsionfree Modules and Related Modules

2021/01/12 by Dey, Souvik, Takahashi, Ryo · 4 citations
#13C60 #13D02 #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2101.04465

Abstract

Let R be a commutative noetherian ring. Denote by mod R the category of finitely generated R-modules. In this paper, we study n-torsionfree modules in the sense of Auslander and Bridger, by comparing them with n-syzygy modules, and modules satisfying Serre's condition (S_n). We mainly investigate closedness properties of the full subcategories of mod R consisting of those modules.

Cited by

• Annihilation of cohomology over one dimensional almost Gorenstein rings
• Structure of modules stably annihilated by a fixed ideal
• On local rings of finite syzygy representation type
• Base change of (Gorenstein) transpose, k-torsionfree modules, and quasi-faithfully flat extensions

Related

• When is a subcategory Serre or torsionfree?
• When are n-syzygy modules n-torsionfree?
• IE-closed subcategories of commutative rings are torsion-free classes
• Classifying subcategories of modules over Noetherian algebras
• When are KE-closed subcategories torsion-free classes?