Modules with locally linearly ordered distributive hulls
SourcetitleJournal of Pure and Applied Algebra
Let R be a commutative ring with identity and M, N are R-modules with M ? N. Then M ? N is said to be distributive if M?(X + Y)=(M ? Y) + (M ? Y), for all submodules, X, Y of N. The extension M ? N is said to be supporting if Mp?0 for all maximal ideals P of R for which Np?0. In this paper we investigate conditions under which an R-module M has a unique maximal distributive and supporting extension D(M) such that for each maximal ideal P of R the set of Rp-submodules of (D(M) M)p is linearly ordered. � 1987.