Enochs, Edgar E.; Jenda, Overtoun M. G.; Torrecillas, Blas Gorenstein flat modules. (English) Zbl 0794.16001 J. Nanjing Univ., Math. Biq. 10, No. 1, 1-9 (1993). 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. Reviewer: F.Théron (Pretoria) Cited in 15 ReviewsCited in 112 Documents MSC: 16D40 Free, projective, and flat modules and ideals in associative algebras 16D50 Injective modules, self-injective associative rings Keywords:Gorenstein rings; Gorenstein flat modules; exact sequences; flat left modules; injective right modules; flat modules PDFBibTeX XMLCite \textit{E. E. Enochs} et al., J. Nanjing Univ., Math. Biq. 10, No. 1, 1--9 (1993; Zbl 0794.16001)