On Radical Formula in Modules over Noncommutative Rings

Abstract

This paper examines the radical formula in noncommutative case and for this

purpose, a generalization of prime submodule is defined. It is proved that

there is a direct connection between one-sided prime ideals and one-sided

prime submodules. Moreover the connections between the intersection

of all one-sided prime submodules and strongly nilpotent elements of a

module are studied.