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Gorenstein \(F{P_n}\)-injective and Gorenstein \(F{P_n}\)-flat modules. (Chinese. English summary) Zbl 1449.16006

Summary: The concepts of Gorenstein \(F{P_n}\)-injective modules and Gorenstein \(F{P_n}\)-flat modules are introduced. We study the basic properties of these two classes of modules firstly and then discuss the \(F{P_n}\)-injective dimension of Gorenstein \(F{P_n}\)-injective modules and the structures of Gorenstein \(F{P_n}\)-injective modules over an \(n\)-coherent ring. Finally, the conditions under which each \(R\)-module is a Gorenstein \(F{P_n}\)-injective module are given.

MSC:

16D40 Free, projective, and flat modules and ideals in associative algebras
16D50 Injective modules, self-injective associative rings
16E10 Homological dimension in associative algebras
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