Coherent subcategories of finitely generated $\Lambda$-modules

TL;DR

This paper investigates properties of wide subcategories in finitely generated modules over artin algebras, linking them to standard modules, stratified algebras, and ring epimorphisms, providing criteria for certain subcategory structures.

Contribution

It establishes new connections between wide subcategories, standard modules, and stratified algebras, and characterizes when subcategories are pres of a projective module.

Findings

Characterization of wide subcategories related to standard modules

Necessary and sufficient conditions for subcategories to be pres of a projective module

Connections between wide subcategories and ring epimorphisms

Abstract

We explore some properties of wide subcategories of the category mod$\,(\Lambda)$ of finitely generated left $\Lambda$-modules, for some artin algebra $\Lambda.$ In particular we look at wide finitely generated subcategories and give a connection with the class of standard modules and standardly stratified algebras. Furthermore, for a wide class $\mathcal{X}$ in mod$\,(\Lambda),$ we give necessary and sufficient conditions to see that $\mathcal{X}=\mathrm{pres}\,(P),$ for some projective $\Lambda$-module $P;$ and finally, a connection with ring epimorphisms is given.