P-Rational Submodules

Maria Mohammed Baher; Muna Abbas Ahmed

doi:10.24996/ijs.2024.65.2.25

Authors

Maria Mohammed Baher Department of Mathematics, College of Science for Women, University of Baghdad, Baghdad, Iraq
Muna Abbas Ahmed Department of Mathematics, College of Science for Women, University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0003-2436-3765

DOI:

https://doi.org/10.24996/ijs.2024.65.2.25

Keywords:

Rational submodules, Pure submodules, P-rational submodules, Essential submodules

Abstract

A submodule N is called rational in M if ( , E(M))=0, where E(M) is the an injective hull of M. Rational submodules have been studied and discussed by many authors such as H.H. Storrer, H. Khabazian, E. Ghashghaei, A. Hajikarimi, M.S. Abbas and M.S. Nayef. The main objective of this paper is to give a new class of submodules named P-rational submodules. This class is contained properly in the class of rational submodules. Several properties of this concept are introduced. The relationships between this class of submodules and some other related concepts are discussed such as essential and quasi-invertible submodules. Other characterizations of the P-rational submodule analogous to those which is known in the concept of the rational submodule are given.