On primary isolated submodules

Document Type : Research Paper

Authors

Department of Mathematics, College of Education for Pure Science, Ibn-Al-Haitham, University of Baghdad, Baghdad, Iraq

Abstract

Let \(L\) be a left module over a ring \(\text{\ S}\) with identity. In this paper, the concept of primary isolated submodules is introduced. We look for relations between this class of submodules and related modules. A number of facts and characterizations that concern is gained. The aim of this work is to introduce and study the primary isolated submodules as a generalization of isolated submodules. A submodule \(A\) of \(L\) is primary isolated if for each proper \(B\) of \(A\), there is a primary submodule \(C\) of \(L\), \(B \subseteq C\) but\(\text{\ A} \nsubseteq C\). Some properties are gained and we look for any relationship between this type of modules and other related modules.

Keywords

[1] G. Ahmed, Some Generalization of Regular Modules, Ph. D. Thesis, College of Science, University of Baghdad, 2015.
[2] G. Ahmed, The primary radical of submodules, Iraqi J. Sci. to appear.
[3] R.L. McCasland and P.F. Smith, On isolated submodules, Commut. Alge. 34(8) (2006) 2977–2988.
[4] P.F. Smith, Primary modules over commutative rings, Glasgow Math. J. 43(1) (2001) 103–111.
[5] R. Wisbauer, Foundations of Modules and Rings Theory, Philadelphia, Gordon and Breach, 1991.
[6] S.M. Yaseen, F-Regular Modules, M.Sc. Thesis, College of Science, University of Baghdad, 1993.
Volume 13, Issue 1
March 2022
Pages 1605-1611
  • Receive Date: 02 November 2021
  • Accept Date: 30 November 2021