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Posner’s second theorem for Jordan ideals in rings with involution. (English) Zbl 1232.16027

Summary: Posner’s second theorem states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. In this paper we extend this result to Jordan ideals of rings with involution. Moreover, some related results are also discussed.

MSC:

16W10 Rings with involution; Lie, Jordan and other nonassociative structures
16W25 Derivations, actions of Lie algebras
16N60 Prime and semiprime associative rings
16U70 Center, normalizer (invariant elements) (associative rings and algebras)
16U80 Generalizations of commutativity (associative rings and algebras)
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References:

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