Artin Algebras of Finite Type and Finite Categories of Δ-Good Modules

Abstract

We give an alternative proof to the fact that, if the square of the infinite radical of the module category of an Artin algebra is equal to zero, then the algebra is of finite type by making use of the theory of postprojective and preinjective partitions. Further, we use this new approach in order to get a characterization of finite subcategories of Δ-good modules of a quasi-hereditary algebra in terms of depth of morphisms similar to a recently obtained characterization of Artin algebras of finite type.

Key Words:

• Delta-good module category
• Postprojective partition
• Quasi-hereditary algebra

2010 Mathematics Subject Classification:

• 16G70
• 16G60

ACKNOWLEDGMENTS

This article is part of the PhD dissertation of the author [7]. The author also would like to thank the referee for the valuable comments which improved the manuscript.