Generalized Skew Derivations with Nilpotent Values in Prime Rings

DOI10.1080/00927872.2012.745868zbMath1296.16048OpenAlexW2019261188MaRDI QIDQ5413981

Shakir Ali, Vincenzo De Filippis, Asma Ali

Publication date: 2 May 2014

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927872.2012.745868

zbMATH Keywords

commutativity theoremsprime ringsLie idealsgeneralized skew derivations

Mathematics Subject Classification ID

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

Related Items (10)

Certain functional identities involving a pair of generalized skew derivations with nilpotent values on Lie ideals ⋮ \(b\)-generalized skew derivations on multilinear polynomials in prime rings ⋮ An Engel condition with skew derivations for one-sided ideals ⋮ Nonadditive strong commutativity preserving maps on rank-k matrices over division rings ⋮ On b-generalized skew derivations having centralizing commutator in prime rings ⋮ The commutativity of prime \(\Gamma\)-rings with generalized skew derivations ⋮ An Engel condition withb-generalized derivations ⋮ A result concerning nilpotent values with generalized skew derivations on Lie ideals ⋮ Skew derivations on partially ordered sets ⋮ An Engel condition with b-generalized derivations for Lie ideals

Cites Work

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• Identities with a single skew derivation.
• Differential identities with automorphisms and antiautomorphisms. II
• Nilpotent and invertible values in semiprime rings with generalized derivations.
• Remarks on derivations on semiprime rings
• Generalized identities with automorphisms
• A note on semiprime rings with derivation
• Generalized skew derivations characterized by acting on zero products.
• Prime rings satisfying a generalized polynomial identity
• Lie structure of prime rings of characteristic 2
• On a Result of Levitzki
• Generalized derivations of left faithful rings
• Generalized skew derivations with nilpotent values on Lie ideals.

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