Skew derivations with annihilating Engel conditions
Copyright policy )Skew derivations with annihilating Engel conditions
Let \(R\) be a noncommutative prime ring. Let \(\sigma\) be an automorphism of \(R\), \(\delta\) be a \(\sigma\)-derivation, and \(a\in R\). The authors prove that if \(a[\delta(x),x]_k=0\) for any \(x\in R\), where \(k\) is a fixed positive integer, then either \(a=0\) or \(\delta=0\), except when \(R=M_2(\text{GF}(2))\). This extends a result of \textit{W.-K. Shiue} [Rend. Circ. Mat. Palermo, II. Ser. 52, No. 3, 505-509 (2003; Zbl 1146.16307)] to the case of skew derivations.
Prime and semiprime associative rings, Other kinds of identities (generalized polynomial, rational, involution), skew derivations, automorphisms, additive maps, Derivations, actions of Lie algebras, prime rings, generalized polynomial identities
Prime and semiprime associative rings, Other kinds of identities (generalized polynomial, rational, involution), skew derivations, automorphisms, additive maps, Derivations, actions of Lie algebras, prime rings, generalized polynomial identities
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