Generalized Supplemented Semimodules

Hayder Sh. Khareeba; Ahmed H. Alwan

doi:10.55529/jecnam.35.28.35

Generalized Supplemented Semimodules

https://doi.org/10.55529/jecnam.35.28.35

Authors

Hayder Sh. Khareeba Department of Mathematics, College of Education for Pure Sciences," University of Thi-Qar, Thi-Qar, Iraq
Ahmed H. Alwan Department of Mathematics, College of Education for Pure Sciences," University of Thi-Qar, Thi-Qar, Iraq

Keywords:

Generalized Supplemented Semimodule, Subtractive Semimodule, Lifting Semimodule.

Abstract

In this work generalized supplemented semimodules are defined which generalize generalized supplemented modules. We investigate some properties of these semimodules. We show that the finite sum of GS-semimodules is GS-semimodule. We also define WGS-semimodules and proved that a semiring is semilocal if and only if every finitely generated semimodule is a WGS-semimodule. Furthermore, we prove that if be a semimodule as well as . Then is a WGS-semimodule if and only if is semisimple.

Published

2023-08-01

How to Cite

Hayder Sh. Khareeba, & Ahmed H. Alwan. (2023). Generalized Supplemented Semimodules. Journal of Electronics, Computer Networking and Applied Mathematics , 3(05), 28–35. https://doi.org/10.55529/jecnam.35.28.35