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arXiv · 1511.08667

Homological Aspects of the Dual Auslander Transpose II

Xi Tang·Zhaoyong Huang
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Abstract

Let $R$ and $S$ be rings and $_Rω_S$ a semidualizing bimodule. We prove that there exists a Morita equivalence between the class of $\infty$-$ω$-cotorsionfree modules and a subclass of the class of $ω$-adstatic modules. Also we establish the relation between the relative homological dimensions of a module $M$ and the corresponding standard homological dimensions of ${\rm Hom}(ω,M)$. 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.

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Xi Tang, Zhaoyong Huang. 2015-11-27. Homological Aspects of the Dual Auslander Transpose II. https://doi.org/10.1215/21562261-3759504

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