Finitistic dimension and restricted injective dimension |
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| Authors: | Dejun Wu |
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| Affiliation: | 1. Department of Mathematics, Shanghai Jiao Tong University, Dong Chuan Road 800, Min Hang, Shanghai, 200240, P.R. China
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| Abstract: | We study the relations between finitistic dimensions and restricted injective dimensions. Let R be a ring and T a left R-module with A = End R T. If R T is selforthogonal, then we show that rid(T A ) ? findim(A A ) ? findim( R T) + rid(T A ). Moreover, if R is a left noetherian ring and T is a finitely generated left R-module with finite injective dimension, then rid(T A ) ? findim(A A ) ? fin.inj.dim( R R)+rid(T A ). Also we show by an example that the restricted injective dimensions of a module may be strictly smaller than the Gorenstein injective dimension. |
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