Rejective subcategories of artin algebras and orders

TL;DR

This paper investigates the structure of rejective subcategories in artin algebras and orders, linking them to ring epimorphisms and using them to construct modules with finite global dimension endomorphism rings.

Contribution

It introduces a new perspective on rejective subcategories via resolution dimension and connects them to ring epimorphisms, extending Auslander's representation dimension.

Findings

Rejective subcategories correspond to surjective ring morphisms.

Chains of rejective subcategories can produce modules with finite global dimension.

The study extends the concept of representation dimension to a new function $r_\Lambda$.

Abstract

We will study the resolution dimension of functorially finite subcategories. The subcategories with the resolution dimension zero correspond to ring epimorphisms, and rejective subcategories correspond to surjective ring morphisms. We will study a chain of rejective subcategories to construct modules with endomorphisms rings of finite global dimension. We apply these result to study a function $r_\Lambda:\mod\Lambda\to\nnn_{\ge0}$ which is a natural extension of Auslander's representation dimension.