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Semiprime rings with nilpotent Lie ring of inner derivations. (English) Zbl 1307.16035

Summary: 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.

MSC:

16W25 Derivations, actions of Lie algebras
16W10 Rings with involution; Lie, Jordan and other nonassociative structures
16N60 Prime and semiprime associative rings
17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
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References:

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