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IMCS/Publications/BASM/Issues/BASM n.3 (31), 1999/

Injective modules with the direct summand intersection property. (English)

Authors: Valcan D.

Abstract

This work gives a series of characterizations of the injective modules with the direct summand intersection property. We will study necessary conditions, sufficient conditions and necessary and sufficient conditions for an injective $R$-module M to have D.S.I.P. We will present some cases in which D.S.I.P. implies S.D.S.I.P., a lattice characterization of $R$-modules with S.D.S.I.P. as well as some specific solutions of Fuchs's new problem referring to those R-modules M for which both $M$ and $\bigoplus_I M$ have D.S.I.P. We will justify through examples the lack of a link between an R-module M and E(M) - its injective envelope, in problem of intersection direct summands.

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