TY - JOUR T1 - Modules with Copure Intersection Property TT - مدول‎های با خاصیت اشتراک هم‌محض JF - khu-mmr JO - khu-mmr VL - 6 IS - 2 UR - http://mmr.khu.ac.ir/article-1-2771-en.html Y1 - 2020 SP - 271 EP - 276 KW - Pure submodule KW - copure submodule KW - copure intersection property. N2 - 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. Every distributive -module has the copure intersection property. Every strong comultiplication -module has the copure intersection property. An -module has the copure intersection property if and only if for each ideal of and copure submodules of we have If is a , then an -module has the copure intersection property if and only if has the copure sum property. Let , where is a submodule of . If has the copure intersection property, then each has the has the copure intersection property. The converse is true if each copure submodule of is fully invariant../files/site1/files/62/12Abstract.pdf M3 10.52547/mmr.6.2.271 ER -