Department of Mathematics, Faculty of Science, Okayama University
Acta Medica Okayama
0030-1566
51
1
2009
ON LIE IDEALS AND LEFT JORDAN σ-CENTRALIZERS OF 2-TORSION-FREE RINGS
EN
Wagner
Cortes
Claus
Haetinger
<p>B. Zalar proved that any left (resp. right) Jordan centralizer on a 2-torsion-free semiprime ring is a left (resp. right) centralizer. We prove this question changing the semiprimality condition on R. The main result of this paper is the following. Let R be a 2-torsionfree ring which has a commutator right (resp. left) nonzero divisor and
let G: R → R be left (resp. right) Jordan σ-centralizer mapping of , where σ is an automorphism of R. Then G is a left (resp. right) -centralizer mapping of R.</p>
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