Covers and Envelopes by V-Gorenstein Modules

ABSTRACT

In this article, we study V-Gorenstein modules relatives to a dualizing module (Enochs et al., in press). These modules constitute a generalization of the well-known Gorenstein modules and at the same time an extension to the noncommutative case of Ω-Gorenstein modules (cf. Enochs and Jenda, 2000a, in press). We show that, under hypothesis of finiteness of projective dimension for flat modules (a property that holds for many rings), covers and envelopes for these classes of modules exist.

Communicated by J. L. Gomez Pardo