Coarsifications of the module isomorphism relation

TL;DR

This paper introduces new equivalence relations on module categories over associative algebras, based on subalgebra restrictions and automorphism actions, providing new insights into module isomorphism classifications.

Contribution

It defines novel equivalence relations on module categories using subalgebra restrictions and automorphisms, expanding the understanding of module isomorphism relations.

Findings

New equivalence relations on $Mod(A)$ are established.

Results relate these relations to module isomorphism classifications.

The relations are defined via subalgebra restrictions and automorphism actions.

Abstract

In this paper new equivalence relations on the category $Mod(A)$ for any associative algebra $A$ and several related results are given. The new equivalence relations are defined using restrictions to subalgebras and the action of algebra automorphisms on modules.