Totally reflexive extensions and modules

Brauer–thrall for Totally Reflexive Modules

Let R be a commutative noetherian local ring that is not Gorenstein. It is known that the category of totally reflexive modules over R is representation infinite, provided that it contains a non-free module. The main goal of this paper is to understand how complex the category of totally reflexive modules can be in this situation. Local rings (R, m) with m3 = 0 are commonly regarded as the stru...

On the Number of Indecomposable Totally Reflexive Modules

In this note, it is proved that over a commutative noetherian henselian non-Gorenstein local ring there are infinitely many isomorphism classes of indecomposable totally reflexive modules, if there is a nonfree cyclic totally reflexive module.

An Existence Results on Positive Solutions for a Remarks on k-Torsionless Modules

Let R be a commutative Noetherian ring. The k-torsionless modules are defined in [7] as a generalization of torsionless and reflexive modules, i.e., torsionless modules are 1-torsionless and reflexive modules are 2-torsionless. Some properties of torsionless, reflexive, and k-torsionless modules are investigated in this paper. It is proved that if M is an R-module such that G-dimR(M)

Totally Reflexive Modules Constructed from Smooth Projective Curves of Genus

In this paper, from an arbitrary smooth projective curve of genus at least two, we construct a non-Gorenstein Cohen-Macaulay normal domain and a nonfree totally reflexive module over it.

Extensions of Baer and quasi-Baer modules