UKRAINIAN MATHEMATICAL JOURNAL, vol.71, no.9, pp.1419-1428, 2020 (SCI-Expanded)
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 (a generalization of the Dedekind domain) both satisfies the radical formula and can be decomposed into a direct sum of torsion and extending modules.