Applications of stratifying systems to the finitistic dimension
Given an Ext-injective stratifying system of A-modules (theta, (Y) over bar, less than or similar to) satisfying that the projective dimension of Y is finite, we prove that the finitistic dimension of the algebra A is equal to the finitistic dimension of the category I(theta) = {X is an element of m...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2006 |
| País: | México |
| Institución: | Universidad Nacional Autónoma de México |
| Repositorio: | Sistema de Información de la Facultad de Ciencias, UNAM |
| OAI Identifier: | oai:repositorio.fciencias.unam.mx:11154/1348 |
| Acceso en línea: | http://hdl.handle.net/11154/1348 |
| Access Level: | acceso abierto |
| Palabra clave: | Mathematics, Applied Mathematics |
| Sumario: | Given an Ext-injective stratifying system of A-modules (theta, (Y) over bar, less than or similar to) satisfying that the projective dimension of Y is finite, we prove that the finitistic dimension of the algebra A is equal to the finitistic dimension of the category I(theta) = {X is an element of mod Lambda : Ext(Lambda)(1) (-, X)vertical bar(F(theta)) = 0}. Moreover, using the theory of stratifying systems we obtain bounds for the finitistic dimension of A. In particular, we get the optimal bound 2n - 2 for the finitistic dimension of a standardly stratified algebra with n simples. (c) 2005 Elsevier B.V. All rights reserved. |
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