Enochs, Edgar E. Remarks on commutative Noetherian rings whose flat modules have flat injective envelopes. (English) Zbl 0657.13010 Port. Math. 45, No. 2, 151-156 (1988). In this paper the author gives various equivalent conditions for a commutative noetherian ring R to have the following property: Every flat R-module F has a flat injective envelope E(F). - He proves for example that this property is satisfied if and only if E(R) is flat, or the full ring of quotients K of R is quasi-Frobenius, or K is an injective envelope of R. Five other equivalent conditions are given. In a last section it is shown that these properties of a ring R are preserved under the ring extensions \(S^{-1}R\), R[X] and \(R[[ X]]\). Here S is a multiplicatively closed subset of R, and X is an indeterminate over R. Reviewer: J.Herzog Cited in 1 Document MSC: 13C11 Injective and flat modules and ideals in commutative rings 13E05 Commutative Noetherian rings and modules 13B02 Extension theory of commutative rings Keywords:noetherian ring; flat injective envelope; ring extensions PDFBibTeX XMLCite \textit{E. E. Enochs}, Port. Math. 45, No. 2, 151--156 (1988; Zbl 0657.13010) Full Text: EuDML