Rejective subcategories of artin algebras and orders

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 $r_Λ:\modΛ\to\nnn_{\ge0}$ which is a natural extension of Auslander's representation dimension.

arXiv comment43 pages

Cited by in corpus (14)

• Strongly quasi-hereditary algebras and rejective subcategories
• Syzygies of Cohen-Macaulay modules over one dimensional Cohen-Macaulay local rings
• The derived and extension dimensions of abelian categories
• Wide subcategories of $d$-cluster tilting subcategories
• Tilting modules and universal localization
• Recollements of Module Categories
• Torsion-simple objects in abelian categories
• On strongly quasi-hereditary algebras
• Contravariantly finite resolving subcategories over commutative rings
• On the abundance of silting modules
• Ring epimorphisms from path algebras to matrix algebras
• Gabriel-Roiter measure, representation dimension and rejective chains
• Constructing Endomorphism Rings of Large Finite Global Dimension
• On the representation dimension of rank 2 group algebras and related algebras