SUBMODUL HAMPIR PRIMA; ON ALMOST PRIME SUBMODULES

DYANA PATTY, Sri Wahyuni

2014 | Disertasi | PROGRAM STUDI S2 MATEMATIKA

In modul theory, we define prime submodules which motivated by the definition of prime ideals in a ring R (i.e assumed that R be an R-module R). Let R be a commutative ring with identity and M be an R-module. A proper submodule N of M is called prime if whenever r 2 R;m 2 M such that rm 2 N then m 2 N or r 2 AnnR(M=N). A prime submodule then generalized as weakly prime submodules. Furthermore, prime submodules and weakly prime submodules generalized as almost prime submodules. Moreover, an R-module M is called a multiplication module if for each submodule N ofM, there exist an ideal I of R so that N = IM. In this tesis, we discuss about almost prime submodules as a new generalization of prime and weakly prime submodules. We also study some characterization of almost prime submodules especially for multiplication modules.

Kata Kunci : PRIME SUBMODULES