Homological dimensions relative to preresolving subcategories II

References

[1] F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, 2nd ed., Grad. Texts in Math. 13, Springer, New York, 1992. 10.1007/978-1-4612-4418-9Search in Google Scholar

[2] T. Araya, R. Takahashi and Y. Yoshino, Homological invariants associated to semi-dualizing bimodules, J. Math. Kyoto Univ. 45 (2005), no. 2, 287–306. 10.1215/kjm/1250281991Search in Google Scholar

[3] M. Auslander and M. Bridger, Stable Module Theory, Mem. Amer. Math. Soc. 94 (1969), 1–146. 10.1090/memo/0094Search in Google Scholar

[4] M. Auslander, I. Reiten and S. O. Smalø, Representation Theory of Artin Algebras, Cambridge Stud. Adv. Math. 36, Cambridge University, Cambridge, 1997. Search in Google Scholar

[5] L. L. Avramov and A. Martsinkovsky, Absolute, relative, and Tate cohomology of modules of finite Gorenstein dimension, Proc. Lond. Math. Soc. (3) 85 (2002), no. 2, 393–440. 10.1112/S0024611502013527Search in Google Scholar

[6] A. Beligiannis and I. Reiten, Homological and homotopical aspects of torsion theories, Mem. Amer. Math. Soc. 188 (2007), no. 883, 1–207. 10.1090/memo/0883Search in Google Scholar

[7] D. Bennis, Rings over which the class of Gorenstein flat modules is closed under extensions, Comm. Algebra 37 (2009), no. 3, 855–868. 10.1080/00927870802271862Search in Google Scholar

[8] D. Bennis, A note on Gorenstein flat dimension, Algebra Colloq. 18 (2011), no. 1, 155–161. 10.1142/S1005386711000095Search in Google Scholar

[9] D. Bennis and N. Mahdou, First, second, and third change of rings theorems for Gorenstein homological dimensions, Comm. Algebra 38 (2010), no. 10, 3837–3850. 10.1080/00927870903286868Search in Google Scholar

[10] D. Bravo, J. Gillespie and M. Hovey, The stable module category of a general ring, preprint (2014), https://arxiv.org/abs/1405.5768. Search in Google Scholar

[11] T. J. Cheatham and D. R. Stone, Flat and projective character modules, Proc. Amer. Math. Soc. 81 (1981), no. 2, 175–177. 10.1090/S0002-9939-1981-0593450-2Search in Google Scholar

[12] N. Ding, Y. Li and L. Mao, Strongly Gorenstein flat modules, J. Aust. Math. Soc. 86 (2009), no. 3, 323–338. 10.1017/S1446788708000761Search in Google Scholar

[13] E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, De Gruyter Exp. Math. 30, Walter de Gruyter, Berlin, 2011. 10.1515/9783110215236Search in Google Scholar

[14] E. E. Enochs and L. Oyonarte, Covers, Envelopes and Cotorsion Theories, Nova Science, New York, 2002. Search in Google Scholar

[15] S. Estrada, A. Iacob and M. A. Pérez, Model structures and relative Gorenstein flat modules and chain complexes, Categorical, Homological and Combinatorial Methods in Algebra, Contemp. Math. 751, American Mathematical Society, Providence (2020), 135–175. 10.1090/conm/751/15084Search in Google Scholar

[16] D. J. Fieldhouse, Character modules, Comment. Math. Helv. 46 (1971), 274–276. 10.1007/BF02566844Search in Google Scholar

[17] R. Göbel and J. Trlifaj, Approximations and Endomorphism Algebras of Modules. Volume 1. Approximations, De Gruyter Exp. Math. 41, Walter de Gruyter, Berlin, 2012. 10.1515/9783110218114Search in Google Scholar

[18] H. Holm, Gorenstein homological dimensions, J. Pure Appl. Algebra 189 (2004), no. 1–3, 167–193. 10.1016/j.jpaa.2003.11.007Search in Google Scholar

[19] H. Holm and P. Jørgensen, Semi-dualizing modules and related Gorenstein homological dimensions, J. Pure Appl. Algebra 205 (2006), no. 2, 423–445. 10.1016/j.jpaa.2005.07.010Search in Google Scholar

[20] H. Holm and D. White, Foxby equivalence over associative rings, J. Math. Kyoto Univ. 47 (2007), no. 4, 781–808. 10.1215/kjm/1250692289Search in Google Scholar

[21] M. Hoshino, Algebras of finite self-injective dimension, Proc. Amer. Math. Soc. 112 (1991), no. 3, 619–622. 10.1090/S0002-9939-1991-1047011-8Search in Google Scholar

[22] C. Huang and Z. Huang, Torsionfree dimension of modules and self-injective dimension of rings, Osaka J. Math. 49 (2012), no. 1, 21–35. Search in Google Scholar

[23] Z. Huang, Proper resolutions and Gorenstein categories, J. Algebra 393 (2013), 142–169. 10.1016/j.jalgebra.2013.07.008Search in Google Scholar

[24] Z. Huang, Homological dimensions relative to preresolving subcategories, Kyoto J. Math. 54 (2014), no. 4, 727–757. 10.1215/21562261-2801795Search in Google Scholar

[25] Z. Huang, Duality pairs induced by Auslander and Bass classes, Georgian Math. J. 28 (2021), no. 6, 867–882. 10.1515/gmj-2021-2101Search in Google Scholar

[26] A. Iacob, Projectively coresolved Gorenstein flat and ding projective modules, Comm. Algebra 48 (2020), no. 7, 2883–2893. 10.1080/00927872.2020.1723612Search in Google Scholar

[27] Z. Liu, Z. Huang and A. Xu, Gorenstein projective dimension relative to a semidualizing bimodule, Comm. Algebra 41 (2013), no. 1, 1–18. 10.1080/00927872.2011.602782Search in Google Scholar

[28] B. H. Maddox, Absolutely pure modules, Proc. Amer. Math. Soc. 18 (1967), 155–158. 10.1090/S0002-9939-1967-0224649-5Search in Google Scholar

[29] F. Mantese and I. Reiten, Wakamatsu tilting modules, J. Algebra 278 (2004), no. 2, 532–552. 10.1016/j.jalgebra.2004.03.023Search in Google Scholar

[30] L. Mao and N. Ding, Gorenstein FP-injective and Gorenstein flat modules, J. Algebra Appl. 7 (2008), no. 4, 491–506. 10.1142/S0219498808002953Search in Google Scholar

[31] J. Šaroch and J. Šťovíček, Singular compactness and definability for Σ-cotorsion and Gorenstein modules, Selecta Math. (N. S.) 26 (2020), no. 2, Paper No. 23. 10.1007/s00029-020-0543-2Search in Google Scholar

[32] W. Song, T. Zhao and Z. Huang, Duality pairs induced by one-sided Gorenstein subcategories, Bull. Malays. Math. Sci. Soc. 43 (2020), no. 2, 1989–2007. 10.1007/s40840-019-00786-wSearch in Google Scholar

[33] W. Song, T. Zhao and Z. Huang, One-sided Gorenstein subcategories, Czechoslovak Math. J. 70(145) (2020), no. 2, 483–504. 10.21136/CMJ.2019.0385-18Search in Google Scholar

[34] B. Stenström, Coherent rings and F⁢P-injective modules, J. Lond. Math. Soc. (2) 2 (1970), 323–329. 10.1112/jlms/s2-2.2.323Search in Google Scholar

[35] X. Tang and Z. Huang, Homological aspects of the dual Auslander transpose, II, Kyoto J. Math. 57 (2017), no. 1, 17–53. 10.1215/21562261-3759504Search in Google Scholar

[36] X. Tang and Z. Huang, Homological invariants related to semidualizing bimodules, Colloq. Math. 156 (2019), no. 1, 135–151. 10.4064/cm7476-3-2018Search in Google Scholar

[37] T. Wakamatsu, On modules with trivial self-extensions, J. Algebra 114 (1988), no. 1, 106–114. 10.1016/0021-8693(88)90215-3Search in Google Scholar

[38] T. Wakamatsu, Stable equivalence for self-injective algebras and a generalization of tilting modules, J. Algebra 134 (1990), no. 2, 298–325. 10.1016/0021-8693(90)90055-SSearch in Google Scholar

[39] T. Wakamatsu, Tilting modules and Auslander’s Gorenstein property, J. Algebra 275 (2004), no. 1, 3–39. 10.1016/j.jalgebra.2003.12.008Search in Google Scholar

[40] C. Xi, On the finitistic dimension conjecture. III. Related to the pair e⁢A⁢e⊆A, J. Algebra 319 (2008), no. 9, 3666–3688. 10.1016/j.jalgebra.2008.01.021Search in Google Scholar