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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.