CHARACTERIZATION OF WEAKLY PRIME SUBMODULES - Nur Afifah, Puspa
Let R be a commutative ring with non-zero identity and M be a unital module. An R-Module M is called multiplication if for each submodule of M is of the form IM for some ideal I of R. We say that I is a presentasion ideal of N. If M is a multiplication module then we can dene the product of two submodules by multiply every presentasion ideals of that submodules respectively, then the result is multiplied by M. So that, the product of two elements can be done in the same way, with assume the elements as cyclic submodules. If N is submodule of M then (N : M) is dened by fr 2 RjrM Ng. If a proper submodule N of M with rm 2 N (r 2 R;m 2 M) implies that either m 2 N or r 2 (N : M), then N is called prime. Then concept of prime submodule was extended to weakly prime submodule, with condition rm 6= 0. Every prime submodule is weakly prime submodule, but the converse is not always true. In this thesis, we will prove characterization of weakly prime submodules.