Biju, V.; Udhayakumar, R.; Umamaheswaran, A.; Parimala, M. The dimension of Gorenstein \(\mathcal{X}_{\mathcal{Y}}\)-flat modules with respect to a semidualizing modules. (English) Zbl 1414.13007 Adv. Stud. Contemp. Math., Kyungshang 28, No. 4, 669-679 (2018). Summary: In this paper, we introduce and investigate the notion of Gorenstein \(\mathcal{X}_{\mathcal{Y}}\)-flat modules with respect to a semidualizing module and also study the relationship between the \(G_C-\mathcal{X}_{\mathcal{Y}}\)-flat resolution and the \(\mathcal{X}_{\mathcal{Y}}\)-flat resolution ofa module over \(G\mathcal{X}_{\mathcal{Y}}f\)-closed ring where \(\mathcal{X}\) is a class of left \(R\)-modules and \(\mathcal{Y}\) is a subclass of \(\mathcal{X}\). MSC: 13D05 Homological dimension and commutative rings 13D07 Homological functors on modules of commutative rings (Tor, Ext, etc.) 18G20 Homological dimension (category-theoretic aspects) 18G25 Relative homological algebra, projective classes (category-theoretic aspects) Keywords:semidualizing module; \(G\mathcal{X}_{\mathcal{Y}}f\)-closed ring; \(G_C\)-\(\mathcal{X}_{\mathcal{Y}}\)-flat module; \(G_C\)-\(\mathcal{X}_{\mathcal{Y}}\)-flat dimension PDFBibTeX XMLCite \textit{V. Biju} et al., Adv. Stud. Contemp. Math., Kyungshang 28, No. 4, 669--679 (2018; Zbl 1414.13007)