On Dense Subsemimodules and Prime Semimodules

Ahmed H.  Alwan; Asaad M. A.  Alhossaini

doi:10.24996/ijs.2020.61.6.24

Authors

Ahmed H. Alwan Department of Mathematics, College of Education for Pure Sciences, Thi-Qar University, Thi-Qar, Iraq
Asaad M. A. Alhossaini Department of Mathematics, College of Education for Pure Sciences, Babylon University, Babylon, Iraq

DOI:

https://doi.org/10.24996/ijs.2020.61.6.24

Keywords:

Semimodule, Semiring, Dense subsemimodule, Invertible ideal, Prime semimodule, Dedekind semidomain

Abstract

In this paper, we study the class of prime semimodules and the related concepts, such as the class of semimodules, the class of Dedekind semidomains, the class of prime semimodules which is invariant subsemimodules of its injective hull, and the compressible semimodules. In order to make the work as complete as possible, we stated, and sometimes proved, some known results related to the above concepts.