Some results on \(G_C\)-flat dimension of modules. (English) Zbl 07144887

Summary: In this paper, we study some properties of \(G_C\)-flat \(R\)-modules, where \(C\) is a semidualizing module over a commutative ring \(R\) and we investigate the relation between the \(G_C\)-yoke with the \(C\)-yoke of a module as well as the relation between the \(G_C\)-flat resolution and the flat resolution of a module over \(GF\)-closed rings. We also obtain a criterion for computing the \(G_C\)-flat dimension of modules.


18G20 Homological dimension (category-theoretic aspects)
18G25 Relative homological algebra, projective classes (category-theoretic aspects)
Full Text: DOI


[1] Bennis D., Rings over which the class of Gorenstein flat modules is closed under extentions, Comm. Algebra 37 (2009), no. 3, 855-868
[2] Christensen L. W., Gorenstein Dimensions, Lecture Notes in Mathematics, 1747, Springer, Berlin, 2000
[3] Christensen L. W.; Frankild A.; Holm H., On Gorenstein projective, injective and flat dimensions a functorial description with applications, J. Algebra 302 (2006), no. 1, 231-279
[4] Enochs E.; Jenda O. M. G., Relative Homological Algebra, De Gruyter Expositions in Mathematics, 30, Walter de Gruyter, Berlin, 2000
[5] Enochs E.; Jenda O. M. G.; Torrecillas B., Gorenstein flat modules, Nanjing Daxue Xuebao Shuxue Bannian Kan 10 (1993), no. 1, 1-9
[6] Foxby H.-B., Gorenstein modules and related modules, Math. Scand. 31 (1972), 267-284
[7] Golod E. S., \(G\)-dimension and generalized perfect ideals, Algebraic geometry and its applications, Trudy Mat. Inst. Steklov. 165 (1984), 62-66 (Russian)
[8] Holm H., Gorenstein homological dimensions, J. Pure Appl. Algebra 189 (2004), no. 1-3, 167-193
[9] Holm H.; Jørgensen P., Semidualizing modules and related Gorenstein homological dimensions, J. Pure. Appl. Algebra 205 (2006), no. 2, 423-445
[10] Holm H.; White D., Foxby equivalence over associative rings, J. Math. Kyoto Univ. 47 (2007), no. 4, 781-808
[11] Huang C.; Huang Z., Gorenstein syzygy modules, J. Algebra 324 (2010), no. 12, 3408-3419
[12] Liu Z.; Yang X., Gorenstein projective, injective and flat modules, J. Aust. Math. Soc. 87 (2009), no. 3, 395-407
[13] Rotman J. J., An Introduction to Homological Algebra, Pure and Applied Mathematics, 85, Academic Press, New York, 1979
[14] Sather-Wagstaff S.; Sharif T.; White D., AB-contexts and stability for Gorenstein flat modules with respect to semidualizing modules, Algebr. Represent. Theory 14 (2011), no. 3, 403-428
[15] Selvaraj C.; Udhayakumar R.; Umamaheswaran A., Gorenstein n-flat modules and their covers, Asian-Eur. J. Math. 7 (2014), no. 3, 1450051, 13 pages
[16] Vasconcelos W. V., Divisor Theory in Module Categories, North-Holland Mathematics Studies, 14, North-Holland Publishing Co., Amsterdam, American Elsevier Publishing Co., New York, 1974
[17] White D., Gorenstein projective dimension with respect to a semidualizing module, J. Commut. Algebra 2 (2010), no. 1, 111-137
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.