Homological Aspects of the Dual Auslander Transpose II

Abstract

Let $R$ and $S$ be rings and ${}_R{\omega }_S$ a semidualizing bimodule. We prove that there exists a Morita equivalence between the class of $\infty$-$\omega$-cotorsionfree modules and a subclass of the class of $\omega$-adstatic modules. Also we establish the relation between the relative homological dimensions of a module $M$ and the corresponding standard homological dimensions of $\mathrm{Hom}(\omega ,M)$. By investigating the properties of the Bass injective dimension of modules (resp. complexes), we get some equivalent characterizations of semi-tilting modules (resp. Gorenstein artin algebras). Finally we obtain a dual version of the Auslander-Bridger's approximation theorem. As a consequence, we get some equivalent characterizations of Auslander $n$-Gorenstein artin algebras.

37 pages, accepted for publication in Kyoto Journal of Mathematics

References in corpus (2)

• Homological Aspects of the Dual Auslander Transpose
• Homological Dimensions Relative to Preresolving Subcategories