Some NECESSARY AND SUFFICIENT CONDITIONS OF COMULTIPLICATION MODULE

Wattimena, Emanuella M C
W.M. Patty, Henry
Patty, Dyana
L. Rahakbauw, Dorteus

Parameter: Jurnal Matematika, Statistika dan Terapannya
Vol 1 No 2 (2022): Parameter: Jurnal Matematika, Statistika dan Terapannya

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.