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The coincidence of the set of all nilpotent elements of a ring with its primeradical has a module analogue which occurs when the zero submodule satisfiesthe radical formula. A ring $R$ is 2-primal if the set of all nilpotentelements of $R$ coincides with its prime radical. This fact motivates our studyin this paper, namely, to compare 2-primal submodules and submodules thatsatisfy the radical formula. A demonstration of the importance of 2-primalmodules in bridging the gap between modules over commutative rings and modulesover noncommutative rings is done and new examples of rings and modules thatsatisfy the radical formula are also given.

A relationship between 2-primal modules and modules that satisfy the radical formula