Some Properties of Left Weakly Jointly Prime (R,S)-Submodules

Dian Ariesta Yuwaningsih

Abstract


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.


Keywords


weakly prime submodule, jointly prime submodule, prime submodule

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References


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DOI: https://doi.org/10.22342/jims.26.2.832.234-241

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