Free $R-module$ over an integral domain R that is not a field has finite length iff it is $0-module$
I try to begin with the most navie case:If $F$ is free $R-module$ on singleton,that is,$R$,I attempt to prove if submodule $M$ is simple,then it must be trivial.But I can't see how to do it..Any hint will be helpful , thanks.