Kyoto Journal of Mathematics

Homological aspects of the dual Auslander transpose, II

Xi Tang and Zhaoyong Huang

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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.

Article information

Source
Kyoto J. Math., Volume 57, Number 1 (2017), 17-53.

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

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1489201229

Digital Object Identifier
doi:10.1215/21562261-3759504

Mathematical Reviews number (MathSciNet)
MR3621778

Zentralblatt MATH identifier
06705666

Subjects
Primary: 16E10: Homological dimension 18G25: Relative homological algebra, projective classes 16E05: Syzygies, resolutions, complexes 16E30: Homological functors on modules (Tor, Ext, etc.)

Keywords
semidualizing bimodules $\infty$-$\omega$-cotorsion-free modules Bass classes $\mathcal{X}$-projective dimension $\mathcal{X}$-injective dimension Bass injective dimension (strong) $\mathrm{Ext}$-cograde (strong) $\mathrm{Tor}$-cograde

Citation

Tang, Xi; Huang, Zhaoyong. Homological aspects of the dual Auslander transpose, II. Kyoto J. Math. 57 (2017), no. 1, 17--53. doi:10.1215/21562261-3759504. https://projecteuclid.org/euclid.kjm/1489201229


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