journal-of-discrete-mathematical-sciences-and-cryptography Journal of Discrete Mathematical Sciences and Cryptography 2169-0065 0972-0529 Taru Publications 10.47974/JDMSC-2380 Pure rationally extending modules Al-Majeed Zahra Moaed Abd Department of Chemical Engineering and Oil Pollution, College of Chemical Engineering, University of Technology, Baghdad, Iraq Shaker Zainab Raad Department of Registration and Student Affairs, University of Technology, Baghdad, Iraq Nayef Mahdi Saleh Department of Mathematics, College of Education, Mustansiriyah University, Baghdad, Iraq 29 5 1991 1996 22 05 2026

The main purpose for this work, we introduce and study a concept for pure rationally extending modules on the class of rationally extending modules by using pure submodules and direct summands. This paper presents the concept of pure rationally extending modules as a more general concept than rationally extending modules. Throughout this study, many examples and counterexamples are given. In addition, many properties, propositions, and relationships between pure rationally extending modules and some other concepts are discussed.

 Extending modules Rationally extending modules Pure extending modules Pure submodules access open retracted no