The Radical of an Endo-Restricted Bounded Submodule Related to Prime Submodules

Mohammed Salman  Murad; Buthyna Najad  Shihab

doi:10.30526/38.4.4130

Authors

Mohammed Salman Murad Department of Mathematics, College of Education for Pure Science, Ibn-AL-Haitham, University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0002-7789-7026
Buthyna Najad Shihab Department of Mathematics, College of Education for Pure Science, Ibn-AL-Haitham, University of Baghdad, https://orcid.org/0000-0002-6553-2089

DOI:

https://doi.org/10.30526/38.4.4130

Keywords:

Endo-R.B submodule, Bounded module, Prime Submodule, Scalar module

Abstract

In this paper, we present the concept of the radical of an Endo-Restricted Bounded submodule and establish its characterization, which is regarded as a new notion. In addition, we study the relationship between the radical of submodules and the radical of an Endo-Restricted Bounded submodules and this connection will give us important results in terms of their radical. Furthermore, this article will demonstrate numerous properties and corollaries that elucidate the concept of the Endo-Restricted Bounded submodule's radical. This work includes a new class of T-module as well as a T-submodule called the Endo-Restricted Bounded Module (submodule), written briefly as the Endo-R.B. module (submodule), provided with some examples that illustrate and clarify in a nice way this type of module (submodule). However, our focus will be on the radicals of the endo-R.B. submodule. Prime submodule and scalar module both play a crucial role in many properties that show the relationship between prime submodules and Endo-R.B submodules. Furthermore, some generalizations of prime submodules, such as S-prime submodules, are involved in this research.

Author Biographies

Mohammed Salman Murad, Department of Mathematics, College of Education for Pure Science, Ibn-AL-Haitham, University of Baghdad, Baghdad, Iraq

Department of Mathematics
Buthyna Najad Shihab, Department of Mathematics, College of Education for Pure Science, Ibn-AL-Haitham, University of Baghdad,

Department of Mathematics

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