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April 2017 Homological aspects of the dual Auslander transpose, II
Xi Tang, Zhaoyong Huang
Kyoto J. Math. 57(1): 17-53 (April 2017). DOI: 10.1215/21562261-3759504

Abstract

Let R and S be rings, and let RωS be a semidualizing bimodule. We prove that there exists a Morita equivalence between the class of -ω-cotorsion-free 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 Hom(ω,M). By investigating the properties of the Bass injective dimension of modules (resp., complexes), we get some equivalent characterizations of semitilting modules (resp., Gorenstein Artin algebras). Finally, we obtain a dual version of the Auslander–Bridger approximation theorem. As a consequence, we get some equivalent characterizations of Auslander n-Gorenstein Artin algebras.

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Xi Tang. Zhaoyong Huang. "Homological aspects of the dual Auslander transpose, II." Kyoto J. Math. 57 (1) 17 - 53, April 2017. https://doi.org/10.1215/21562261-3759504

Information

Received: 11 June 2015; Revised: 24 November 2015; Accepted: 26 November 2015; Published: April 2017
First available in Project Euclid: 11 March 2017

zbMATH: 06705666
MathSciNet: MR3621778
Digital Object Identifier: 10.1215/21562261-3759504

Subjects:
Primary: 16E05, 16E10, 16E30, 18G25

Rights: Copyright © 2017 Kyoto University

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Vol.57 • No. 1 • April 2017
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