Abstract
This paper gives a definition of a new class of T-module and T-submodule called an Endo-Restricted Bounded module (submodule) written shortly by Endo-R.B. module (submodule) and present some different approaches to connect this class of module with other types of modules such as: compressible modules, monoform modules, critically compressible modules, retractable modules, and quasi-Dedekind modules. One of the main purpose of this work is to introduce a few new conditions and reveal some properties and corollaries. This paper considered to be another solution or answer for Zelmanowitz’s problem. In fact, an Endo-R.B. T-module plays an important role to this problem and we say under what condition compressible T-module would be a critically compressible T-module so we present a positive solution depend on an Endo-R.B module. The T-homomorphism of compressible and monoform modules join in a nice way with an endomorphism of a T-module Ω that we need it for the definition of an Endo-R.B module. Moreover, an Endo-R.B module gives us directly three different modules and these modules are bounded module, finitely annihilated module, and retractable module. Finally, polyform and fully polyform modules are involved in this article.
Recommended Citation
Murad, Mohammed Salman and Shihab, Buthyna Najad
(2025)
"A New Class of Endo-R.B Module and Its Relationship with Modules,"
Iraqi Journal for Computer Science and Mathematics: Vol. 6:
Iss.
2, Article 15.
DOI: https://doi.org/10.52866/2788-7421.1256
Available at:
https://ijcsm.researchcommons.org/ijcsm/vol6/iss2/15
