On Pure Multiplication Modules - Younis Ghawi, Tha’ar (Al-Qadisiyah Journal of Pure Science, 2017)
Let R be a commutative ring with identity and M be a unitary left R-module. A submodule N of an R-module M is called pure if, IN ï€½ N ïƒ‡IM for all ideal I of R. In this paper, we shall investigate and study some various properties of the concept of pure multiplication modules, which is appeared in [3] as a proper generalization of multiplication modules, where an R-module M is called pure multiplication if for every pure submodule N of M there exists an ideal I of R such that N ï€½ IM . We give a number of results concerning pure multiplication modules. Also, we discussed some properties of pure submodules of pure multiplication modules.