SEMI-RADICALS OF SUB MODULES IN MODULES

LetR be a commutative ring and M be a unitary R− module. We define a semiprime submodule of a module and consider various properties of it. Also wedefine semi-radical of a submodule of a module and give a number of its properties. We define modules which satisfy the semi-radical formula ( ) . . . . s t s r f and present the existence of such a module.

Keywords:

Prime sub module , semiprime sub module , radical and semi- radical of a module , modules satisfying the semi-radical formula