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Gorenstein flat modules. (English) Zbl 0794.16001

The motivation for this paper were the analogous results that have been found for Gorenstein injective (resp. projective) and usual injective (resp. projective) modules.
If \(R\) is any ring, a left \(R\)-module \(M\) is said to be Gorenstein flat if and only if there is an exact sequence \(\cdots\to F^{-1}\to F^ 0\to F^ 1\to\cdots\) of flat left \(R\)-modules such that the sequence remains exact when \(E\otimes-\) is applied to it for any injective right \(R\)-module \(E\) and such that \(M=\ker(F^ 0\to F^ 1)\). Several equivalent conditions for an \(R\)-module to be Gorenstein flat are found for the case where \(R\) is an \(n\)-Gorenstein ring with \(n\geq 3\). These results are analogous to those for the usual flat modules.

MSC:

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