𝓦-RESOLUTIONS AND GORENSTEIN CATEGORIES WITH RESPECT TO A SEMIDUALIZING BIMODULES

Title & Authors
𝓦-RESOLUTIONS AND GORENSTEIN CATEGORIES WITH RESPECT TO A SEMIDUALIZING BIMODULES
YANG, XIAOYAN;

Abstract
Let $\small{\mathcal{W}}$ be an additive full subcategory of the category R-Mod of left R-modules. We provide a method to construct a proper $\small{{\mathcal{W}}^H_C}$-resolution (resp. coproper $\small{{\mathcal{W}}^T_C}$-coresolution) of one term in a short exact sequence in R-Mod from those of the other two terms. By using these constructions, we introduce and study the stability of the Gorenstein categories $\small{{\mathcal{G}}_C({\mathcal{W}}{\mathcal{W}}^T_C)}$ and $\small{{\mathcal{G}}_C({\mathcal{W}}^H_C{\mathcal{W}})}$ with respect to a semidualizing bimodule C, and investigate the 2-out-of-3 property of these categories of a short exact sequence by using these constructions. Also we prove how they are related to the Gorenstein categories $\small{{\mathcal{G}}((R{\ltimes}C){\otimes}_R{\mathcal{W}})_C}$ and $\small{{\mathcal{G}}(Hom_R(R{\ltimes}C,{\mathcal{W}}))_C}$ over $\small{R{\ltimes}C}$.
Keywords
$\small{\mathcal{W}}$-resolution and $\small{\mathcal{W}}$-coresolution;Gorenstein category;
Language
English
Cited by
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