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\(n\)-cotorsion modules and \(n\)-flat modules. (English) Zbl 1424.16009

Summary: In this paper, we introduce \(n\)-cotorsion modules and study some properties of them. Over right \(n\)-coherent rings, we prove that the class of \(n\)-cotorsion left \(R\)-modules is enveloping. Furthermore, we prove that the class of \(n\)-flat left \(R\)-modules is covering and preenveloping and investigate the \(n\)-flat dimensions induced by \(n\)-flat precovers and preenvelopes.

MSC:

16D40 Free, projective, and flat modules and ideals in associative algebras
16E10 Homological dimension in associative algebras
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