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The dimension of Gorenstein \(\mathcal{X}_{\mathcal{Y}}\)-flat modules with respect to a semidualizing modules. (English) Zbl 1414.13007

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)
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