Some Properties of Left Weakly Jointly Prime (R,S)-Submodules
| Main Author: | Yuwaningsih, Dian Ariesta |
|---|---|
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
IndoMS
, 2020
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| Subjects: | |
| Online Access: |
http://www.jims-a.org/index.php/jimsa/article/view/832 http://www.jims-a.org/index.php/jimsa/article/view/832/pdf |
Daftar Isi:
- Let R and S be commutative rings with identity. A proper (R,S)submodule P of M is called a left weakly jointly prime if for each element a and b in R and (R,S)-submodule K of M with abKS ⊆ P implies either aKS ⊆ P or bKS ⊆ P. In this paper, we present some properties of left weakly jointly prime (R,S)-submodule. We show some necessary and sufficient condition of left weakly jointly prime (R,S)-submodule. Moreover, we present that every left weakly jointly prime (R,S)-submodule contains a minimal left weakly jointly prime (R,S)submodule. At the end of this paper, we also show that in left multiplication (R,S)-module, every left weakly jointly prime (R,S)-submodule is equal to jointly prime (R,S)-submodules.