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Filtering subcategories of modules of an artinian algebra
- Publication Year :
- 2015
-
Abstract
- Let $A$ be an artinian algebra, and let $\mathcal{C}$ be a subcategory of mod$A$ that is closed under extensions. When $\mathcal{C}$ is closed under kernels of epimorphisms (or closed under cokernels of monomorphisms), we describe the smallest class of modules that filters $\mathcal{C}$. As a consequence, we obtain sufficient conditions for the finitistic dimension of an algebra over a field to be finite. We also apply our results to the torsion pairs. In particular, when a torsion pair is induced by a tilting module, we show that the smallest classes of modules that filter the torsion and torsion-free classes are completely compatible with the quasi-equivalences of Brenner and Butler.<br />Comment: 22 pages
- Subjects :
- Mathematics - Representation Theory
16E10, 16G10, 16P20
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1505.07025
- Document Type :
- Working Paper