Browse > Article
http://dx.doi.org/10.4134/JKMS.j210579

GORENSTEIN QUASI-RESOLVING SUBCATEGORIES  

Cao, Weiqing (School of Mathematics and Statistics Jiangsu Normal University)
Wei, Jiaqun (School of Mathematical Sciences Nanjing Normal University)
Publication Information
Journal of the Korean Mathematical Society / v.59, no.4, 2022 , pp. 733-756 More about this Journal
Abstract
In this paper, we introduce the notion of Gorenstein quasiresolving subcategories (denoted by 𝒢𝒬𝓡𝒳 (𝓐)) in term of quasi-resolving subcategory 𝒳. We define a resolution dimension relative to the Gorenstein quasi-resolving categories 𝒢𝒬𝓡𝒳 (𝓐). In addition, we study the stability of 𝒢𝒬𝓡𝒳 (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 𝒢𝒬𝒳-projective A-module M.
Keywords
${\mathcal{GQ_X}}$-projective objects; ${\mathcal{GQR_X(A)}}$-resolution; stability; finitistic dimension; endomorphism algebras;
Citations & Related Records
연도 인용수 순위
  • Reference
1 M. Behboodi, A. Ghorbani, A. Moradzadeh-Dehkordi, and S. H. Shojaee, C-pure projective modules, Comm. Algebra 41 (2013), no. 12, 4559-4575. https://doi.org/10.1080/00927872.2012.705934   DOI
2 N. Ding, Y. Li, and L. Mao, Strongly Gorenstein flat modules, J. Aust. Math. Soc. 86 (2009), no. 3, 323-338. https://doi.org/10.1017/S1446788708000761   DOI
3 S. Eilenberg and J. C. Moore, Foundations of relative homological algebra, Mem. Amer. Math. Soc. 55 (1965), 39 pp.
4 L. Mao and N. Ding, Gorenstein FP-injective and Gorenstein flat modules, J. Algebra Appl. 7 (2008), no. 4, 491-506. https://doi.org/10.1142/S0219498808002953   DOI
5 S. Sather-Wagstaff, T. Sharif, and D. White, Stability of Gorenstein categories, J. Lond. Math. Soc. (2) 77 (2008), no. 2, 481-502. https://doi.org/10.1112/jlms/jdm124   DOI
6 J. Wei, Finitistic dimension and restricted flat dimension, J. Algebra 320 (2008), no. 1, 116-127. https://doi.org/10.1016/j.jalgebra.2008.03.017   DOI
7 A. Zhang, Finitistic dimension and endomorphism algebras of Gorenstein projective modules, arXiv:1802.00669.
8 M. Auslander and M. Bridger, Stable module theory, Memoirs of the American Mathematical Society, No. 94, American Mathematical Society, Providence, RI, 1969.
9 L. W. Christensen, H.-B. Foxby, and A. Frankild, Restricted homological dimensions and Cohen-Macaulayness, J. Algebra 251 (2002), no. 1, 479-502. https://doi.org/10.1006/jabr.2001.9115   DOI
10 E. E. Enochs and O. M. G. Jenda, Gorenstein injective and projective modules, Math. Z. 220 (1995), no. 4, 611-633. https://doi.org/10.1007/BF02572634   DOI
11 E. E. Enochs and O. M. G. Jenda, Relative homological algebra, De Gruyter Expositions in Mathematics, 30, Walter de Gruyter & Co., Berlin, 2000. https://doi.org/10.1515/9783110803662   DOI
12 E. E. Enochs, O. M. G. Jenda, and J. A. Lopez-Ramos, Covers and envelopes by V - Gorenstein modules, Comm. Algebra 33 (2005), no. 12, 4705-4717. https://doi.org/10.1080/00927870500328766   DOI
13 S. M. Fakhruddin, Pure-injective modules, Glasgow Math. J. 14 (1973), 120-122. https://doi.org/10.1017/S0017089500001853   DOI
14 X. Zhu, The homological theory of quasi-resolving subcategories, J. Algebra 414 (2014), 6-40. https://doi.org/10.1016/j.jalgebra.2014.05.018   DOI
15 H. Holm, Gorenstein homological dimensions, J. Pure Appl. Algebra 189 (2004), no. 1-3, 167-193. https://doi.org/10.1016/j.jpaa.2003.11.007   DOI
16 J. Simmons, Cyclic-purity: a generalization of purity for modules, Houston J. Math. 13 (1987), no. 1, 135-150.