Some results on the quotient of co-m modules

Let R be a commutative ring with identity and let M be a unitary R-module. In this paper, among various results, we prove that if M is a cancellation R-module and L is a nonzero simple submodule of M, then L is a copure submodule of M. Moreover, in this case, if M is co-m, then M/L is also a co-m R-module. We investigate various conditions under which the quotient module M/N of a co-m M is also a co-m. We prove that if M is a cancellation Noetherian co-m module, then for every second submodule N of M the quotient module M/N is a co-m R-module. We obtain some results concerning socle and radical of co-m modules.

Keywords:

comultiplication module , Small submodule , quasi-copure submodule