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2015 Gorenstein categories $\mathcal G(\mathscr X,\mathscr Y,\mathscr Z)$ and dimensions
Xiaoyan Yang
Rocky Mountain J. Math. 45(6): 2043-2064 (2015). DOI: 10.1216/RMJ-2015-45-6-2043

Abstract

Let $\mathscr {A}$ be an abelian category and $\mathscr {X},\mathscr {Y},\mathscr {Z}$ additive full subcategories of $\mathscr {A}$. We introduce and study the Gorenstein category $\mathcal {G}(\mathscr {X},\mathscr {Y},\mathscr {Z})$ as a common generalization of some known modules such as Gorenstein projective (injective) modules \cite {EJ95}, strongly Gorenstein flat modules \cite {DLM} and Gorenstein FP-injective modules \cite {DM}, and prove the stability of $\mathcal {G}(\mathscr {X},\mathscr {Y},\mathscr {Z})$. We also establish Gorenstein homological dimensions in terms of the category $\mathcal {G}(\mathscr {X},\mathscr {Y},\mathscr {Z})$.

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Xiaoyan Yang. "Gorenstein categories $\mathcal G(\mathscr X,\mathscr Y,\mathscr Z)$ and dimensions." Rocky Mountain J. Math. 45 (6) 2043 - 2064, 2015. https://doi.org/10.1216/RMJ-2015-45-6-2043

Information

Published: 2015
First available in Project Euclid: 14 March 2016

zbMATH: 1336.18005
MathSciNet: MR3473166
Digital Object Identifier: 10.1216/RMJ-2015-45-6-2043

Subjects:
Primary: 18G20, 18G25

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

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Vol.45 • No. 6 • 2015
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