On Finite Unions of Submodules

Abstract

This paper is concerned with finite unions of ideals and modules. The first main result is that, if N ⊆ N ₁ ∪ N ₂ ∪ … ∪ N _s is a covering of a module N by submodules N _i , such that all but two of the N _i are intersections of strongly irreducible modules, then N ⊆ 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.

Key Words:

• Ideal
• Submodule
• Union

2010 Mathematics Subject Classification:

• 13

Notes

Communicated by S. Goto.