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On surjective linear maps preserving commutativity

Published online by Cambridge University Press:  12 July 2007

K. I. Beidar  and
Ying-Fen Lin
K. I. Beidar
Affiliation:
Department of Mathematics, National Cheng-Kung University, Tainan, Taiwan
Ying-Fen Lin
Affiliation:
Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan
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Abstract

We describe surjective linear maps preserving commutativity from (symmetric elements of) any algebra (with involution) onto (symmetric elements of) a prime algebra (with involution) not satisfying polynomial identities of low degree. Bijective commutativity preservers on skew elements of centrally closed prime algebras with involution of the first kind are also investigated.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 6 , December 2004 , pp. 1023 - 1040
Copyright
Copyright © Royal Society of Edinburgh 2004

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