Rejective subcategories of artin algebras and orders

2003/11/17 by Osamu Iyama, Iyama, Osamu
Mathematics · #16E10 #16G10 #16G30 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:16E10 #msc:16G10 #msc:16G30

paper · pdf · doi:10.48550/arxiv.math/0311281

43 pages

arxiv created 2003/11/17 · arxiv updated 2009/12/01

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→\nnn_≥0 which is a natural extension of Auslander's representation dimension.

Related

• A functorial approach to categorical resolutions
• Filtering subcategories of modules of an artinian algebra
• The radical of functorially finite subcategories
• Derived dimensions of representation-finite algebras
• Categorical resolutions of a class of derived categories