Strong commutativity preserving maps on Lie ideals of semiprime rings

Details Strong commutativity preserving maps on Lie ideals of semiprime rings Strong commutativity preserving maps on Lie ideals of semiprime rings

2009-02-04

arxiv.org/abs/0902.0808v1

Beitrage zur algebra und geometrie 49 (2) (2008) 441--447

Mathematics

Rings and Algebras

7 pages

Scientific paper

Let $R$ be a 2-torsion free semiprime ring and $U$ a nonzero square closed
Lie ideal of $R$. In this paper it is shown that if $f$ is either an
endomorphism or an antihomomorphism of $R$ such that $f(U)=U,$ then $f$ is
strong commutativity preserving on $U$ if and only if $f$ is centralizing on
$U.$

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