A UNIFIED APPROACH TO VARIOUS GORENSTEIN MODULES

Renyu Zhao; Yanjie Li

doi:10.1216/rmj.2022.52.2229

Abstract

Let $\mathcal V,\mathcal W,\mathcal Y,\mathcal X$ be four classes of modules. We introduce a notion of $(\mathcal V,\mathcal W,\mathcal Y,\mathcal X)$ -Gorenstein modules which unifies a number of well-known Gorenstein modules. Under certain mild assumptions on the classes $(\mathcal V,\mathcal W,\mathcal Y,\mathcal X)$ , we first study properties of $(\mathcal V,\mathcal W,\mathcal Y,\mathcal X)$ -Gorenstein modules. Then, we apply the obtained results to establish the Foxby equivalences associate to $(\mathcal V,\mathcal W,\mathcal Y,\mathcal X)$ -Gorenstein modules. Many results on the Gorenstein modules involved in this general setting can be obtained as corollaries.

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Renyu Zhao. Yanjie Li. "A UNIFIED APPROACH TO VARIOUS GORENSTEIN MODULES." Rocky Mountain J. Math. 52 (6) 2229 - 2246, December 2022. https://doi.org/10.1216/rmj.2022.52.2229

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Received: 15 April 2021; Revised: 23 February 2022; Accepted: 8 March 2022; Published: December 2022

First available in Project Euclid: 28 December 2022

MathSciNet: MR4527020

zbMATH: 1509.18011

Digital Object Identifier: 10.1216/rmj.2022.52.2229

Subjects:

Primary: 18G25

Secondary: 18B05 , 18G20

Keywords: Foxby equivalence , Gorenstein module , semidualizing bimodule

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