Generalizations of Supplemented and Lifting Semimodules - Alwan, Ahmed H. (Iraqi Journal of Science, 2024)
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.