IMI/Publicaţii/BASM/Ediţii/BASM n.3 (37), 2001/

Again on the direct sums of modules with the direct summand intersection property.

Authors: Vălcan Dumitru


We say that an R-module (abelian group) M has the direct summand intersection property (in short D.S.I.P.) if the intersection of any two direct summands of M is again a direct summand in M. In 1997 L.Fuchs proposes the following problem for solving: “Find necessary and/or sufficient conditions over an R-module M (specifically an abelian group) to that, being given any index set I (finite or infinite) the R-module M*=⊕IM to have D.S.I.P.” In this work we will present other solutions to this problem, different from the previously known ones.