In this work, we prove by employing mapping Cone that the sequence and the subsequence of the characteristic-zero are exact and subcomplex respectively in the case of partition (6,6,4) .
Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if
the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple , semisimple) F- submodules and quotient F- modules are introduced and given some properties .