CHARACTERIZATION OF ALMOST PRIME SUBMODULES AND ITS LOCALIZATION

• Main Author: (NIM: 20116024), STEVEN
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/31104
• Institution: Institut Teknologi Bandung

Prime submodules were arised as similar notions to prime ideals of a ring. The study of prime submodules of a module over a commutative ring with identity is growing since the 20th century by giving the characterization of prime submodules structure. On the other hand, the research of prime submodules began to produce the generalization of that notion. Some generalizations and related notions that will be studied in this research are weakly prime submodules, fully prime modules, primal submodules and almost prime submodules which is the main notion in this research. On the other hand, some researchers have developed a notion about ring and module localization. In this research, we will study some characterization of almost prime submodule and define new generalization of it, which is S(N)-almost prime submodules. This study have five main results. First, reviewing some characterization of almost prime submodules as the theoritical basis for this research. Second, giving some new characterizations of almost prime submodules. Third, giving some new characterizations and relation of fully prime modules and strongly prime submodules. Fourth, generalizing the notion of almost prime submodules in the localization and its similar notions in ideals, furthermore giving its characterization. Lastly, showing the relation between almost prime submodules in its localization and its residual ideals.