#### 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*(*x*^{m+n+1}) =
*x*^{m}
*T*(*x*) *x*^{n}

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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