Ukr. Mat. Zh. - 2019. - 71, № 9. - pp. 1241-1248
We determine some classes of left modules satisfying the radical formula in a noncommutative ring. We also show that, under a certain condition, a finitely generated module over an $HNP$-ring (the generalization of Dedekind domain) both satisfies the radical formula and can be decomposed into a direct sum of torsion modules and extending modules.