Annihilator large-superfluous submodules. Issue 1 (March 2021)

• Record Type: Journal Article
• Authors: Abbas, M. S.
• Is Part Of: Journal of physics. Volume 1818:Issue 1(2021)
• Publication Date: 2021-03
• Subjects: large-superfluous submodules -- annihilators -- annihilator-superfluous submodules -- annihilator large-superfluous submodules; Physics -- Congresses; 530.5
• DOI: 10.1088/1742-6596/1818/1/012084
• Languages: English
• ISSNs: 1742-6588

Abstract

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.