Pure-minimal chain complexes

TL;DR

This paper introduces pure-minimality for chain complexes, showing its equivalence to homotopic minimality in standard cases and highlighting its usefulness for complexes of flat modules, with applications in ring characterization.

Contribution

It defines pure-minimality for chain complexes and demonstrates its advantages over traditional minimality, especially for flat modules, with applications in ring theory.

Findings

Pure-minimality coincides with homotopic minimality in standard settings.

Pure-minimality is particularly useful for complexes of flat modules.

Characterizations of von Neumann regular rings and left perfect rings are provided.

Abstract

We introduce a notion of pure-minimality for chain complexes of modules and show that it coincides with (homotopic) minimality in standard settings, while being a more useful notion for complexes of flat modules. As applications, we characterize von Neumann regular rings and left perfect rings.