Main Article Content
Abstract
We introduce the concepts of $\beta$-prime submodules and weakly $\beta$-prime submodules of unital left modules over a commutative ring with nonzero identity. Some properties of these concepts are investigated. We use the notion of the product of two submodules to characterize $\beta$-prime submodules of a multiplication module. Characterization of $\beta$-prime and weakly $\beta$-prime submodules of arbitary modules are also given.
Article Details
How to Cite
Khumprapussorn, T. (2019). On Beta-Prime Submodules. Journal of the Indonesian Mathematical Society, 25(2), 128–138. https://doi.org/10.22342/jims.25.2.759.128-138
References
- begin{thebibliography}{99}
- bibitem{1} Ameri, R.: On the prime submodules of multiplication modules, {em International Journal of Mathematics and Mathematical Sciences}, textbf{27} (2003), 1715-1724.
- bibitem{2} Atani, S.E., Farzalipour, F.: On weakly prime submodules, {em Tamkang
- Journal of Mathematics}, textbf{38}(3) (2007), 247-252.
- bibitem{3} El-Bast, Z., Smith, P.F.: Multiplication modules, {em Communications in Algebra}, textbf{16}(4) (1988), 755-779.
- end{thebibliography}
References
begin{thebibliography}{99}
bibitem{1} Ameri, R.: On the prime submodules of multiplication modules, {em International Journal of Mathematics and Mathematical Sciences}, textbf{27} (2003), 1715-1724.
bibitem{2} Atani, S.E., Farzalipour, F.: On weakly prime submodules, {em Tamkang
Journal of Mathematics}, textbf{38}(3) (2007), 247-252.
bibitem{3} El-Bast, Z., Smith, P.F.: Multiplication modules, {em Communications in Algebra}, textbf{16}(4) (1988), 755-779.
end{thebibliography}