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Cover Gorenstein \(AC\)-flat dimensions. (Chinese. English summary) Zbl 1474.16030

Summary: By introducing the covering Gorenstein \(AC\)-flat dimension of modules, the conditions under which Gorenstein \(AC\)-flat modules are closed under extension are discussed, and a sufficient condition for the stability of Gorenstein \(AC\)-flat modules is given. Some properties of Gorenstein \(AC\)-flat modules, and some stability conditions of Gorenstein \(AC\)-flat modules are improved.

MSC:

16E10 Homological dimension in associative algebras
16D40 Free, projective, and flat modules and ideals in associative algebras
16E65 Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
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