Posner's second theorem for Jordan ideals in rings with involution.

DOI10.1016/J.EXMATH.2011.07.002zbMath1232.16027OpenAlexW1987453230MaRDI QIDQ654961

Lahcen Oukhtite

Publication date: 28 December 2011

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.exmath.2011.07.002

zbMATH Keywords

commutativity theoremsgeneralized derivationsrings with involution*-prime ringsJordan idealscentralizing 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 (27)

On Posner’s second theorem for semirings with involution ⋮ Commuting-like elements in prime rings with derivations ⋮ Composition and orthogonality of derivations with multilinear polynomials in prime rings ⋮ Semiderivations satisfying certain algebraic identities on Jordan ideals. ⋮ Structure of a quotient ring R/P and its relation with generalized derivations of R ⋮ Differential identities on prime rings with involution ⋮ Commutativity theorems for *-prime rings with differential identities on Jordan ideals. ⋮ Generalized derivations of order 2 on multilinear polynomials in prime rings ⋮ Commutativity theorems in rings with involution ⋮ Unnamed Item ⋮ Some commutativity theorems for rings with involution involving generalized derivations ⋮ Some commutativity criteria for prime rings with differential identities on Jordan ideals ⋮ Certain algebraic identities on prime rings with involution ⋮ On $^*$-differential identities in prime rings with involution ⋮ Derivations satisfying certain algebraic identities on Jordan ideals. ⋮ Generalized \((\alpha ,\beta )\)-derivations on Jordan ideals in \(*\)-prime rings. ⋮ Unnamed Item ⋮ On generalized derivations and Jordan ideals of prime rings ⋮ Center-like subsets in prime rings with derivations and endomorphisms ⋮ Higher derivations and Posner's second theorem for semiprime rings ⋮ New classes of endomorphisms and some classification theorems ⋮ Center-like subsets in rings with derivations or endomorphisms ⋮ Unnamed Item ⋮ Unnamed Item ⋮ A note on derivations and Jordan ideals of prime rings ⋮ Unnamed Item ⋮ Identities involving skew Lie product and a pair of generalized derivations in prime rings with involution

Cites Work

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• Commutativity conditions on derivations and Lie ideals in \(\sigma\)-prime rings.
• On Jordan ideals and left \((\theta,\theta)\)-derivations in prime rings.
• Lie and Jordan Structure in Prime Rings with Derivations
• Derivations in Prime Rings
• Posner's Second Theorem Deduced from the First

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