This paper is concerned with finite unions of ideals and modules. The first main result is that if N ⊆ N1 ∪N2 ∪ · · · ∪Ns is a covering of a module N by submodules Ni, such that all but two of the Ni are intersections of strongly irreducible modules, then N ⊆ Nk for some k. The special case when N is a multiplication module is considered. The second main result generalizes earlier results on co...

For a group G and N-series G of G let In R,G(G), n ≥ 0, denote the filtration of the group algebra R(G) induced by G , and IR(G) its augmentation ideal. For subgroups H of G , left ideals J of R(H) and right H -submodules M of IZZ(G) the quotients IR(G)J/MJ are studied by homological methods, notably for M = IZZ(G)IZZ(H), IZZ(H)IZZ(G) + IZZ([H,G])ZZ(G) and ZZ(G)IZZ(N) + In ZZ,G(G) with N CG whe...

let r be a commutative ring with non-zero identity and m be a unital r-module. then the concept of quasi-secondary submodules of m is introduced and some results concerning this class of submodules is obtained

The paper uses a new approach to investigate prime submodules and minimal prime submodules of certain modules such as Artinian and torsion modules. In particular, we introduce a concrete formula for the radical of submodules of Artinian modules.

in this paper we introduce the notion of classical quasi-primary submodules that generalizes the concept of classical primary submodules. then, we investigate decomposition and minimal decomposition into classical quasi-primary submodules. in particular, existence and uniqueness of classical quasi-primary decompositions in finitely generated modules over noetherian rings are proved. moreover, w...