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Finitistic dimension and restricted injective dimension

Dejun Wu (2015)

Czechoslovak Mathematical Journal

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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