SEMIMODUL PRIMA PENUH - Muhammad Anwar, Andi
The dissertation’s area is about a fully prime semimodules. At the beginning of its development, the study of the concept of prime starts from the structure of ideal in the ring. The prime ideals are introduced by Dedekind. It is extended by Goldie to the ring’s structure and then by Feller and Swokowski to the module’s structure. The fully prime concept is a development of the prime concept. Since semimodules are a weaker structure of modules, the results obtained in fully prime modules can be applied to semimodules. In addition, in this research, we will try to characterize fully prime semimodules based on their subsemimodules and ideals in their semiring. This dissertation is an extension of the results obtained in fully prime modules. In research by Behboodi et al. obtained equivalence of fully prime modules related to homogeneous semisimple modules, prime cyclic submodules, semiprime cyclic submodules, maximal submodules, semisimple modules, descending chain conditions in finitely generated submodules, and the Socle from their modules. Not all equivalence in fully prime modules satisfies to fully prime semimodules, so some conditions are required in semimodules. This dissertation also examines the relationship between fully prime semimodules and fully prime semirings.