Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2022; 59(4): 733-756

Published online July 1, 2022 https://doi.org/10.4134/JKMS.j210579

Copyright © The Korean Mathematical Society.

Gorenstein quasi-resolving subcategories

Weiqing Cao, Jiaqun Wei

Jiangsu Normal University; Nanjing Normal University

Abstract

In this paper, we introduce the notion of Gorenstein quasi-resolving subcategories (denoted by $\mathcal{GQR}_{\mathcal{X}}(\mathcal{A})$) in term of quasi-resolving subcategory $\mathcal{X}$. We define a resolution dimension relative to the Gorenstein quasi-resolving categories $\mathcal{GQR}_{\mathcal{X}}(\mathcal{A})$. In addition, we study the stability of $\mathcal{GQR}_{\mathcal{X}}(\mathcal{A})$ and apply the obtained properties to special subcategories and in particular to modules categories. Finally, we use the restricted flat dimension of right $B$-module $M$ to characterize the finitistic dimension of the endomorphism algebra $B$ of a $\mathcal{GQ}_{\mathcal{X}}$-projective $A$-module $M$.

Keywords: $\mathcal{GQ}_{\mathcal{X}}$-projective objects, $\mathcal{GQR}_{\mathcal{X}}(\mathcal{A})$-resolution, stability, finitistic dimension, endomorphism algebras

MSC numbers: Primary 16D10, 16E05, 16E10, 18G10

Supported by: Weiqing Cao was supported by the Science Foundation of Jiangsu Normal University (No. 21XFRS024). Jiaqun Wei was supported by the National Natural Science Foundation of China (Grant No. 11771212) and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.