Finitistic Dimension through Infinite Projective Dimension
نویسندگان
چکیده
We show that an artin algebra Λ having at most three radical layers of infinite projective dimension has finite finitistic dimension, generalizing the known result for algebras with vanishing radical cube. We also give an equivalence between the finiteness of fin.dim.Λ and the finiteness of a given class of Λ-modules of infinite projective dimension.
منابع مشابه
Comparison of Views on Finitistic Projective Dimension
The finitistic dimension conjecture says that the projective dimension of finitely generated modules over an Artin algebra is bounded when finite. The conjecture is known for algebras of representation dimension 3, for modules of Loevey length 2 and for stratifying systems with at most 2 indecomposable modules of infinite projective dimension (Huard, Lanzilotta, Mendoza [4]). We would like to i...
متن کاملA Quillen Model Structure Approach to the Finitistic Dimension Conjectures
We explore the interlacing between model category structures attained to classes of modules of finite X -dimension, for certain classes of modules X . As an application we give a model structure approach to the Finitistic Dimension Conjectures and present a new conceptual framework in which these conjectures can be studied. Let Λ be a finite dimensional algebra over a field k (or more generally...
متن کامل(n, m)-Strongly Gorenstein Projective Modules
This paper is a continuation of the papers J. Pure Appl. Algebra, 210 (2007), 437–445 and J. Algebra Appl., 8 (2009), 219–227. Namely, we introduce and study a doubly filtered set of classes of modules of finite Gorenstein projective dimension, which are called (n, m)-strongly Gorenstein projective ((n, m)-SG-projective for short) for integers n ≥ 1 and m ≥ 0. We are mainly interested in studyi...
متن کاملFinitistic Dimension and a Homological Generalization of Semi-primary Rings
Introduction. If P is a ring and M a left P-module, then homological algebra attaches three dimensions to M, projective, weak, and injective(1)By taking the supremum of one of these dimensions as M ranges over all left P-modules, one obtains one of the left "global" dimensions of R. Auslander and Buchsbaum [3] and, subsequently, Serre [14], found it relevant and fruitful, in the study of commut...
متن کاملProperly stratified algebras and tilting
We study the properties of tilting modules in the context of properly stratified algebras. In particular, we answer the question when the Ringel dual of a properly stratified algebra is properly stratified itself, and show that the class of properly stratified algebras for which the characteristic tilting and cotilting modules coincide is closed under taking the Ringel dual. Studying stratified...
متن کامل