Suatu Generalisasi (R,S)-Submodul Prima Gabungan

Abstract

Let R and S be commutative rings with unity and M be an (R,S)-module. A proper (R,S)-submodule P of M is called a jointly prime (R,S)-submodule if for each ideal I of R, ideal J of S, and (R,S)-submodule N of M satisfy INJ ⊆ P implies IMJ ⊆ P or N ⊆ P . In this paper, we will present the definition of one generalization of jointly prime (R,S)-submodules, that is called left weakly jointly prime (R,S)-submodules. Furthermore,we will show some properties about the relationship between left weakly jointly prime (R,S)-submodules and jointly prime