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Applications of stratifying systems to the finitistic dimension |
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| Authors: | Eduardo do N Marcos Corina Sáenz |
| Institution: | a Departamento de Matemática, Universidade de São Paulo, Caixa Postal 66.281, São Paulo, SP 05315-970, Brasil b Instituto de Matemáticas, U.N.A.M., Circuito Exterior, Ciudad Universitaria, C.P. 04510, Mexico, D.F. México c Departamento de Matemáticas, Facultad de Ciencias, U.N.A.M., Circuito Exterior, Ciudad Universitaria, C.P. 04510, México, D.F. Mexico |
| Abstract: | Given an Ext-injective stratifying system of Λ-modules  satisfying that the projective dimension of Y is finite, we prove that the finitistic dimension of the algebra Λ is equal to the finitistic dimension of the category  . Moreover, using the theory of stratifying systems we obtain bounds for the finitistic dimension of Λ. In particular, we get the optimal bound 2n-2 for the finitistic dimension of a standardly stratified algebra with n simples. |
| Keywords: | 16E09 16W99 17B10 |
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