On surjective linear maps preserving commutativity

DOI10.1017/S0308210500003619zbMath1074.16019OpenAlexW2098453450MaRDI QIDQ4653535

Ying-Fen Lin, Kostia I. Beidar

Publication date: 7 March 2005

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500003619

zbMATH Keywords

prime algebrasextended centroidscommutativity preserving mapssymmetric elements, skew-symmetric elements

Mathematics Subject Classification ID

Prime and semiprime associative rings (16N60) Automorphisms and endomorphisms (16W20) Other kinds of identities (generalized polynomial, rational, involution) (16R50) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Linear transformations, semilinear transformations (15A04) Center, normalizer (invariant elements) (associative rings and algebras) (16U70)

Related Items (11)

On maps preserving zero Jordan products. ⋮ Nonlinear strong commutativity preserving maps on skew elements of prime rings with involution. ⋮ Functional identities and their applications ⋮ Strong commutativity preserving generalized derivations on right ideals. ⋮ Commutativity preserving maps revisited. ⋮ An extension of the Gleason-Kahane-Żelazko theorem: A possible approach to Kaplansky's problem ⋮ Konstantin Igorevich Beidar (1951-2004) ⋮ Strong commutativity preserving generalized derivations on Lie ideals ⋮ Preserving Zeros of a Polynomial ⋮ Strong commutativity preserving maps in prime rings with involution. ⋮ On maps preserving zeros of the polynomial \(xy - yx^\ast\)

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