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.
Universitatea "Babes-Bolyai"
str. M.Kogalniceanu, 1, 3400 Cluj-Napoca, România
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