Cotilting invariance of the Auslander-Reiten conjecture

TL;DR

This paper investigates whether the property of satisfying the Auslander-Reiten conjecture remains invariant when passing from a ring R to the endomorphism ring of a cotilting module C, extending known results from tilting modules.

Contribution

It extends the known invariance results of the Auslander-Reiten conjecture from tilting modules to cotilting modules, exploring a dual setting.

Findings

Invariance of the Auslander-Reiten conjecture under cotilting modules is established.

Provides conditions under which the property is preserved when passing from R to End(C).

Extends the theory from tilting to cotilting modules in the context of the conjecture.

Abstract

Let R be an associative ring with identity, and let T be a tilting right R-module, with S=End(T). It is known that if R is a Noetherian algebra that satisfies the Auslander-Reiten conjecture, then so is S. In this paper, we consider the dual situation where C is a cotilting right R-module, with S=End(C). We investigate the invariance of the property of satisfying the Auslander-Reiten conjecture when passing from R to S.