Generalizations of Supplemented and Lifting Semimodules

Ahmed H.  Alwan

doi:10.24996/ijs.2024.65.7.27

Authors

Ahmed H. Alwan Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq https://orcid.org/0000-0003-4367-4606

DOI:

https://doi.org/10.24996/ijs.2024.65.7.27

Keywords:

Supplemented (δ-supplemented) semimodules, Principally supplemented (δ-supplemented) semimodules, Principally lifting (δ-lifting) semimodules, Semiperfect semimodules

Abstract

In this paper, principally supplemented (-supplemented), and principally lifting (-lifting) semimodules are defined as generalizations of principally supplemented (-supplemented), and principally lifting (-lifting) modules. Let be a semiring. An -semimodule is called a principally supplemented (-supplemented) semimodule, if for all there exists a subsemimodule of with and small (-small) in . In this paper, we examine properties of principally -supplemented semimodules and generalize results on principally -supplemented modules to semimodules. Besides, we characterize -semiperfect semimodules as a generalization of -semiperfect modules.