Isomorphisms between strongly triangular matrix rings

TL;DR

This paper characterizes isomorphisms between strongly triangular matrix rings, showing their behavior parallels that of idempotents in semiperfect rings, and provides a method to compute their automorphism groups.

Contribution

It introduces a detailed description of isomorphisms for strongly triangular matrix rings and offers a theoretical approach to determine their automorphism groups.

Findings

Isomorphisms behave like idempotents in semiperfect rings

Provides a method to compute automorphism groups

Establishes structural parallels with semiperfect rings

Abstract

We describe isomorphisms between strongly triangular matrix rings that were defined earlier in Berkenmeier et al. (2000) as ones having a complete set of triangulating idempotents, and we show that the so-called triangulating idempotents behave analogously to idempotents in semiperfect rings. This study yields also a way to compute theoretically the automorphism groups of such rings in terms of corresponding automorphism groups of certain subrings and bimodules involved in their structure.