Ring epimorphisms from path algebras to matrix algebras

TL;DR

This paper investigates ring epimorphisms and universal localisations from path algebras to matrix algebras, focusing on their construction through extension from smaller to larger path algebras.

Contribution

It introduces methods for constructing ring epimorphisms and universal localisations by extending from smaller to larger path algebras, generalizing initial results.

Findings

Constructed explicit ring epimorphisms between path algebras and matrix algebras.

Extended known results to broader classes of path algebras.

Provided generalizations for the construction process.

Abstract

In this text, we are concerned with ring epimorphisms, and more specifically universal localisations, from path algebras to matrix algebras. We are mainly focused on constructing ring epimorphisms and universal localisations by extending them from from smaller path algebras to larger path algebras. At first, we discuss some simple results, and then we present generalizations thereof in several directions.