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.

中文翻译：

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非交换环的根本公式

我们在非交换环中确定满足根式的一些左模类。我们还表明，在一定条件下，在 HNP 环（Dedekind 域的推广）上的有限生成模块既满足自由基公式，又可以分解为扭转和扩展模块的直接和。