Co-absolutely co-pure modules

Abstract

B. Maddox [15] defined absolutely pure modules and derived some interesting properties of these modules. C. Megibben [17] continued the study of these modules and found more interesting properties. We introduce in this paper co-absolutely co-pure modules as dual to absolutely pure modules. We first prove that over a commutative classical ring these modules are precisely the flat modules. As a biproduct we get a projective characterization of flat modules over a commutative co-noetherian ring. Secondly, over a quasi-Frobenius ring R, co-absolutely co-pure right R-modules turn out to be projective modules. Finally we get a characterization of almost Dedekind domains in terms of co-absolutely co-pure modules.