Z-Small Submodules and Z-Hollow Modules

  • Amina T. Hamad Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
  • Alaa A. Elewi Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
Keywords: small submodules, hollow modules, supplement submodules, essential ideals

Abstract

A submodule Ϝ of an R-module Ε is called small in Ε if whenever  , for some submodule W of Ε , implies  . In this paper , we introduce the notion of Ζ-small submodule , where a proper submodule Ϝ of an R-module Ε is said to be Ζ-small in Ε if  , such that  , then  , where  is the second singular submodule of Ε . We give some properties of Ζ-small submodules . Moreover , by using this concept , we generalize the notions of hollow modules , supplement submodules, and supplemented modules into Ζ-hollow modules, Ζ-supplement submodules, and Ζ-supplemented modules. We study these concepts and provide some of their relations .

Published
2021-08-31
How to Cite
Hamad, A. T., & Elewi, A. A. (2021). Z-Small Submodules and Z-Hollow Modules. Iraqi Journal of Science, 62(8), 2708-2713. https://doi.org/10.24996/ijs.2021.62.8.24
Section
Mathematics