Title of article :
End-ᴪ-Prime Submodules
Author/Authors :
al-mothafar, nuhad s. university of baghdad - collage of science - department of mathematic, Iraq , abdil -khalik, adwia j. al-mustansiriya university. - college of science - dept. of mathematics, Iraq
Abstract :
Let R be a commutative ring with identity and M an unitary R-module. Let (M) be theset of all submodules of M, and ᴪ: (M) (M) be a function. We say that a propersubmodule P of M is end-ᴪ-prime if for each EndR(M) and x M, if (x) P, theneither x £ P + ᴪ(P) or a(M) P + ᴪ(P). Some of the properties of this concept will beinvestigated. Some characterizations of end-ᴪ-prime submodules will be given, and we showthat under some assumtions prime submodules and end--prime submodules are coincide.
Keywords :
Prime submodules , S , prime submodules , ᴪ , prime submodules , end , , primesubmodules
Journal title :
Ibn Alhaitham Journal For Pure and Applied Science
Journal title :
Ibn Alhaitham Journal For Pure and Applied Science
