Coherent subcategories of finitely generated $\Lambda$-modules

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.