Some NECESSARY AND SUFFICIENT CONDITIONS OF COMULTIPLICATION MODULE

Abstract

In ring theory, if  and  be ideals of , then the multiplication of  and , which is defined by  is also ideal of . Motivated by the multiplication of two ideals, then can be defined a multiplication module, a special module which every submodule of  can be expressed as the multiplication of an ideal of ring and the module itself, and can simply be written as .  Furthermore, if   the module become a comultiplication module. By the definition, it concludes that every comultiplication module is a multiplication module but the converse is not necessarily applicable.

Keywords:  annihilator, ideal, module, comultiplication module, multiplication module, ring, submodule.