journal-of-discrete-mathematical-sciences-and-cryptography Journal of Discrete Mathematical Sciences and Cryptography 2169-0065 0972-0529 Taru Publications 10.47974/JDMSC-2680 Endo-greatly bounded modules and module homomorphisms Hussein Sattar Kamel Department of Mathematics, College of Education for Pure Science (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq Shihab Buthyna Najad Department of Mathematics, College of Education for Pure Science (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq 29 5 2083 2087 22 05 2026

The class of π‘šπ‘œπ‘‘π‘’π‘™π‘’s is introduced in this paper. We study and discuss the classes for the π‘šπ‘œπ‘‘π‘’π‘™π‘’, named Endo-Greatly Bounded module, which is briefly introduced as (Endo-G.B. π‘šπ‘œπ‘‘π‘’π‘™π‘’s) and π‘šπ‘œπ‘‘π‘’π‘™π‘’s Homomorphism. It also gives some examples and properties. Moreover, we studied relations among this type of π‘šπ‘œπ‘‘π‘’π‘™π‘’s and certain π‘šπ‘œπ‘‘π‘’π‘™π‘’s, such as Prime π‘šπ‘œπ‘‘π‘’π‘™π‘’s, compressible π‘šπ‘œπ‘‘π‘’π‘™π‘’s, monoform π‘šπ‘œπ‘‘π‘’π‘™π‘’s, retractable π‘šπ‘œπ‘‘π‘’π‘™π‘’s, and quasi-Dedekind π‘šπ‘œπ‘‘π‘’π‘™π‘’s. We present results that are proven to explain this relationship. In this paper, compressible and monoform π‘šπ‘œπ‘‘π‘’π‘™π‘’s play a major role in order to obtain Β Endo-G.B. π‘šπ‘œπ‘‘π‘’π‘™π‘’s. Also, retractable π‘šπ‘œπ‘‘π‘’π‘™π‘’s and a quasi-Dedekind π‘šπ‘œπ‘‘π‘’π‘™π‘’ are both related to Β Endo-G.B. π‘šπ‘œπ‘‘π‘’π‘™π‘’s, we shall show this relationship.

 Endo-greatly bounded module Compressible modules Quasi-dedekind modules access open retracted no