Generalizations of Supplemented and Lifting Semimodules
Supplemented (δ-supplemented) semimodules
Principally supplemented (δ-supplemented) semimodules
Principally lifting (δ-lifting) semimodules
Semiperfect semimodules
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.