End á´ª -Prime Submodules

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Nuhad S. AL-Mothafar
Adwia J. Abdil -Khalik

Abstract

      Let R be a commutative ring with identity and M  an unitary R-module. Let ï¤(M)  be the set of all submodules of M, and ï¹: ï¤(M)  ï¤(M)  {ï¦} be a function. We say that a proper submodule P of M is end-ï¹-prime if for each ï¡ ïƒŽ EndR(M) and x  M, if ï¡(x)  P, then either x  P + ï¹(P) or ï¡(M) ïƒ P + ï¹(P). Some of the properties of this concept will be investigated. Some characterizations of end-ï¹-prime submodules will be given, and we show that under some assumtions prime submodules and end-ï¹-prime submodules are coincide.

Article Details

How to Cite
AL-Mothafar, N. S., & Abdil -Khalik, A. J. (2017). End á´ª -Prime Submodules. Ibn AL- Haitham Journal For Pure and Applied Sciences, 29(2), 262–270. Retrieved from https://jih.uobaghdad.edu.iq/index.php/j/article/view/115
Section
mathematics