Finitistic dimension and endomorphism algebras of 𝒲-Gorenstein modules

Abstract

Let [Formula: see text] be an artin algebra, [Formula: see text] be a [Formula: see text]-Gorenstein [Formula: see text]-module and [Formula: see text], then [Formula: see text] is a [Formula: see text]-[Formula: see text]-bimodule. We use the restricted flat dimension of [Formula: see text] and the finitistic [Formula: see text]-dimension of [Formula: see text] to characterize the finitistic dimension of [Formula: see text], and obtain the following main result: if [Formula: see text] is [Formula: see text]-finite with [Formula: see text], then we have: (1) If [Formula: see text] or [Formula: see text], then [Formula: see text] (2) If [Formula: see text], then [Formula: see text]