Equivalence classes of Wakamatsu tilting modules and preenveloping and precovering subcategories

TL;DR

This paper introduces an equivalence relation on Wakamatsu tilting modules over rings, extending key theorems from Artin algebras to general associative rings.

Contribution

It defines a new equivalence relation on Wakamatsu tilting modules and generalizes Mantese Reiten theorems beyond Artin algebras.

Findings

Extended Mantese Reiten theorems to arbitrary associative rings

Introduced an equivalence relation on Wakamatsu tilting modules

Provided new insights into tilting theory over rings

Abstract

Let R be an associative ring with identity. We introduce an equivalence relation on the class of Wakamatsu tilting right R modules. By using this equivalence relation, we extend the Mantese Reiten theorems from the setting of Artin algebras to that of arbitrary associative rings.