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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