Annihilator large-superfluous submodules

Abstract

In this paper, we investigate certain class of submodules which contains that of superfluous submodules. A submodule W of an R-module M is annihilator large-superfluous, if ℓS(V) ≠ 0 implies that W + V ≠ M where V is a large in M and S = End R(M). Several properties and characterizations of such submodules are consider. For α∈ S, we study under what conditions the image of α, Im(α) being annihilator large – superfluous submodule in M. We show that WS(M) = { α∈ S │Im(α) is annihilator large-superfluous in M } equal to { α∈ S │ lm(α) is large-superfluous } under certain class of projectivity. The sum ER (M) of all such submodules of M contains Je(M) and Zs(M). If M is cyclic, then ER(M) is the unique largest annihilator large-superfluous in M. MSC (2010): Primary: 16010; Secondary 16080.