ON FINITE UNIONS OF SUBMODULES

摘要

This paper is concerned with finite unions of ideals and modules. The first main result is that, if N subset of N-1 boolean OR N-2 boolean OR ... boolean OR N-s is a covering of a module N by submodules N-i, such that all but two of the N, are intersections of strongly irreducible modules, then N subset of N-k for some k. The special case when N is a multiplication module is considered. The second main result generalizes earlier results on coverings by primary submodules. In the last section unions of cosets is studied.