Glasnik Matematicki, Vol. 39, No.1 (2004), 21-26.
A REMARK ON CENTRALIZERS IN SEMIPRIME RINGS
Irena Kosi-Ulbl
Department of Mathematics, University of Maribor,
PEF, Koroska c. 160, 2000 Maribor, Slovenia
e-mail: irena.kosi@uni-mb.si
Abstract. The purpose of this paper is to prove the
following result: Let m
≥ 1,
n ≥ 1
be fixed integers and let R be
a (m + n + 2)!-torsion free semiprime ring with the
identity element. Suppose there exists an additive mapping
T : R
→
R, such that
T(xm+n+1) =
xm
T(x) xn
holds for all x
∈ R.
In this case T is a centralizer.
2000 Mathematics Subject Classification.
16N60, 39B05.
Key words and phrases. Prime ring, semiprime ring, left
(right) centralizer, left (right) Jordan centralizer, centralizer.
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