Rejective subcategories of artin algebras and orders

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 $r_{\mathrm{\Lambda }}:\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{\Lambda }\to {\text{nnn}}_{\ge 0}$ which is a natural extension of Auslander’s representation dimension.