Some Properties of Left Weakly Jointly Prime (R,S)-Submodules
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.
Full text article
References
Adkins, W.A., Algebra ”An Approach via Module Theory”, Springer-Verlag, New York, Inc., USA, 1992.
Azizi, A., Weakly Prime Submodules and Prime Modules, Glasgow Mathematics Journal, No.48, 343-346 (2006).
Azizi, A., On Prime and Weakly Prime Submodules, Vietnam Journal of Mathematics, Vol.36 No.3, 315-325 (2008).
Behboodi, M., Koohy, H., Weakly Prime Modules, Vietnam Journal of Mathematics Vol. 32 No. 2, pp. 185 -195 (2004).
Behboodi, M., On Weakly Prime Radical of Modules and Semi-Compatible Modules, Acta Math. Hungarian, Vol 113 No 3, 243-254 (2006).
Dauns, J., Prime Modules, Journal fur die reine und angewandte Mathematik, No. 298, 156-181 (1978).
Khumprapussorn, T., Pianskool, S., and Hall, M., (R,S)-Modules and Theri Fully and Jointly Prime Submodules, International Mathematical Forum, Vol. 7 No. 33, 1631-1643 (2012).
Yuwaningsih, D.A. and Wijayanti, I.E., On Jointly Prime Radicals of (R,S)-Modules, Journal of Indonesian Mathematical Society, Vol.21 No.1, 25-34 (2015).
Authors
Article Details
