Rocky Mountain Journal of Mathematics

Gorenstein categories $\mathcal G(\mathscr X,\mathscr Y,\mathscr Z)$ and dimensions

Xiaoyan Yang

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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 $\mathcal {G}(\mathscr {X},\mathscr {Y},\mathscr {Z})$.

Article information

Rocky Mountain J. Math., Volume 45, Number 6 (2015), 2043-2064.

First available in Project Euclid: 14 March 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 18G20: Homological dimension [See also 13D05, 16E10] 18G25: Relative homological algebra, projective classes

resolution and coresolution Gorenstein category


Yang, Xiaoyan. Gorenstein categories $\mathcal G(\mathscr X,\mathscr Y,\mathscr Z)$ and dimensions. Rocky Mountain J. Math. 45 (2015), no. 6, 2043--2064. doi:10.1216/RMJ-2015-45-6-2043.

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