  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.
