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http://dx.doi.org/10.4134/JKMS.2016.53.1.001

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

YANG, XIAOYAN (DEPARTMENT OF MATHEMATICS NORTHWEST NORMAL UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.53, no.1, 2016 , pp. 1-17 More about this Journal
Abstract
Let $\mathcal{W}$ be an additive full subcategory of the category R-Mod of left R-modules. We provide a method to construct a proper ${\mathcal{W}}^H_C$-resolution (resp. coproper ${\mathcal{W}}^T_C$-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 ${\mathcal{G}}_C({\mathcal{W}}{\mathcal{W}}^T_C)$ and ${\mathcal{G}}_C({\mathcal{W}}^H_C{\mathcal{W}})$ 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 ${\mathcal{G}}((R{\ltimes}C){\otimes}_R{\mathcal{W}})_C$ and ${\mathcal{G}}(Hom_R(R{\ltimes}C,{\mathcal{W}}))_C$ over $R{\ltimes}C$.
Keywords
$\mathcal{W}$-resolution and $\mathcal{W}$-coresolution; Gorenstein category;
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