Posner's second theorem, multilinear polynomials and vanishing derivations

DOI10.1017/S1446788700009915zbMath1059.16024OpenAlexW2046708900MaRDI QIDQ4818760

Vincenzo De Filippis, Onofrio Mario di Vincenzo

Publication date: 1 October 2004

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1446788700009915

zbMATH Keywords

derivationsprime ringsdifferential identitiescentral polynomials

Mathematics Subject Classification ID

Prime and semiprime associative rings (16N60) Other kinds of identities (generalized polynomial, rational, involution) (16R50) Derivations, actions of Lie algebras (16W25) Center, normalizer (invariant elements) (associative rings and algebras) (16U70)

Related Items (13)

Centralizers of generalized skew derivations on multilinear polynomials ⋮ Vanishing Derivations and Centralizers of Generalized Derivations on Multilinear Polynomials ⋮ Right sided ideals and multilinear polynomials with derivation on prime rings. ⋮ Composition and orthogonality of derivations with multilinear polynomials in prime rings ⋮ Derivations vanishing identities involving generalized derivations and multilinear polynomial in prime rings ⋮ An identity on generalized derivations involving multilinear polynomials in prime rings ⋮ Generalized derivations and multilinear polynomials in prime rings ⋮ Generalized derivations of order 2 on multilinear polynomials in prime rings ⋮ On Some Generalized Identities with Derivations on Multilinear Polynomials ⋮ Unnamed Item ⋮ Derivations vanishing on commutators with generalized derivation of order 2 in prime rings ⋮ A result concerning generalized derivations on multilinear polynomials in prime rings ⋮ An Engel condition with skew derivations.

Cites Work

• Unnamed Item
• The additive subgroup generated by a polynomial
• Differential identities of prime rings
• Lie ideals and derivations of prime rings
• Prime nonassociative algebras
• Prime rings satisfying a generalized polynomial identity
• Derivations in Prime Rings
• Nil and Power-Central Polynomials in Rings
• An Engel Condition with Derivation
• Derivations With Invertible Values on a Multilinear Polynomial
• Derivations with Engel conditions on multilinear polynomials
• Derivations on multilinear polynomials in semiprime rings

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