Rocky Mountain Journal of Mathematics

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

Xiaoyan Yang

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

Article information

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

Dates
First available in Project Euclid: 14 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1457960346

Digital Object Identifier
doi:10.1216/RMJ-2015-45-6-2043

Mathematical Reviews number (MathSciNet)
MR3473166

Zentralblatt MATH identifier
1336.18005

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

Keywords
resolution and coresolution Gorenstein category

Citation

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. https://projecteuclid.org/euclid.rmjm/1457960346


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References

  • M. Auslander and M. Bridger, Stable module theory, Memoirs American Mathematical Society 94, 1969.
  • D. Bennis and K. Ouarghi, $\mathcal{X}$-Gorenstein projective modules, Inter. Math. Forum 5 (2010), 487–491.
  • N. Ding and Y. Li and L. Mao, Strongly Gorenstein flat modules, J. Aust. Math. Soc. 66 (2009), 323–338.
  • N. Ding and L. Mao, Gorenstein FP-injective and Gorenstein flat modules, J. Alg. Appl. 7 (2008), 491–506.
  • E.E. Enochs and O.M.G. Jenda, Gorenstein injective and projective modules, Math. Z. 220 (1995), 611–633.
  • E.E. Enochs, O.M.G. Jenda and J.A. López-Ramos, Covers and envelopes by $V$-Gorenstein modules, Comm. Algebra 33 (2005), 4705–4717.
  • H. Holm, Gorenstein homological dimensions, J. Pure Appl. Alg. 189 (2004), 167–193.
  • Z. Huang, Proper resolutions and Gorenstein categories, J. Alg. 393 (2013), 142–169.
  • F. Meng and Q. Pan, $\mathcal{X}$-Gorenstein projective and $\mathcal{Y}$-Gorenstein projective modules, Hacettepe J. Math. Stat. 40 (2011), 537–554.
  • S. Sather-Wagstaff, T. Sharif and D. White, Stability of Gorenstein categories, J. Lond. Math. Soc. 77 (2008), 481–502.