Rings with nilpotent derivations of index ≤ 2

  • M.P. Lukashenko Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
Keywords: derivation, semiprime ring
Published online: 2014-07-19

Abstract


We prove that a semiprime ring with nilpotent derivations (respectively inner derivations) is differentially trivial (respectively commutative). The Jacobson radical $J(R)$ of a ring $R$ with nilpotent derivations contains all its nilpotent elements.

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