Modules with Copure Intersection Property (پژوهش‌های ریاضی, 2020)
Paper pages (271-276) Introduction ‎Throughout this paper‎,  will denote a commutative ring with‎ ‎identity and  will denote the ring of integers. Let be an -module‎. A submodule  of is said to be pure if for every ideal of .  has the copure sum property if the sum of any two copure submodules is again copure‎.  is said to be a comultiplication module if for every submodule of  there exists an ideal  of such that .  satisfies the double annihilator conditions if for each ideal  of , we have . is said to be a strong comultiplication module if  is a comultiplication R-module which satisfies the double annihilator conditions. A submodule  of  is called fully invariant if for every endomorphism  ,. In [5]‎, ‎H‎. ‎Ansari-Toroghy and F‎. ‎Farshadifar introduced the dual notion of pure submodules (that is copure submodules) and investigated the first properties of this class of modules‎. ‎A submodule  of  is said to be copure if  for every ideal of . Material and methods We say that an -modulehas the copure intersection property if the intersection of any two copure submodules is again copure‎. In this paper, we investigate the modules with the copure intersection property and obtain some related results. Conclusion The following conclusions were drawn from this research.