×

Remarks on commutative Noetherian rings whose flat modules have flat injective envelopes. (English) Zbl 0657.13010

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

MSC:

13C11 Injective and flat modules and ideals in commutative rings
13E05 Commutative Noetherian rings and modules
13B02 Extension theory of commutative rings
PDFBibTeX XMLCite
Full Text: EuDML