From ring epimorphisms to universal localisations

TL;DR

This paper explores the relationship between ring epimorphisms and universal localisations, providing conditions under which epimorphisms are universal localisations and examining their impact on derived categories.

Contribution

It offers new criteria for identifying universal localisations among ring epimorphisms and analyzes their influence on recollements of derived module categories.

Findings

Provided sufficient conditions for ring epimorphisms to be universal localisations.

Analyzed recollements induced by homological ring epimorphisms.

Investigated when these recollements extend to derived categories.

Abstract

For a fixed ring, different classes of ring epimorphisms and localisation maps are compared. In fact, we provide sufficient conditions for a ring epimorphism to be a universal localisation. Furthermore, we consider recollements induced by some homological ring epimorphisms and investigate whether they yield recollements of derived module categories.