Suchergebnisse

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.

The aim of this paper is to introduce the concept of Dedekind semimodules and study the related concepts, such as the class of semimodules, and Dedekind multiplication semimodules . And thus study the concept of the embedding of a semimodule in another semimodule.

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.