Some results on the quotient of co-m modules

Abstract

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.