Rings with nilpotent derivations of index ≤ 2

M.P. Lukashenko

doi:10.15330/cmp.6.1.91-95

Rings with nilpotent derivations of index ≤ 2

Authors

M.P. Lukashenko Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine

https://doi.org/10.15330/cmp.6.1.91-95

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.