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Prime and semiprime rings with symmetric skew n-derivations

Ajda Fošner (2014)

Colloquium Mathematicae

Let n ≥ 3 be a positive integer. We study symmetric skew n-derivations of prime and semiprime rings and prove that under some certain conditions a prime ring with a nonzero symmetric skew n-derivation has to be commutative.

Prime modules.

John Dauns (1978)

Journal für die reine und angewandte Mathematik

Semiprime rings with nilpotent Lie ring of inner derivations

Kamil Kular (2014)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

We give an elementary and self-contained proof of the theorem which says that for a semiprime ring commutativity, Lie-nilpotency, and nilpotency of the Lie ring of inner derivations are equivalent conditions

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