The Radical of an Endo-Restricted Bounded Submodule Related to Prime Submodules - Murad, Mohammed Salman; Shihab, Buthyna Najad (Ibn AL-Haitham Journal For Pure and Applied Sciences, 2025)
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.