#### Glasnik Matematicki, Vol. 38, No.2 (2003), 253-261.

### AN EQUATION RELATED TO CENTRALIZERS
IN SEMIPRIME RINGS

### Joso Vukman and Irena Kosi-Ulbl

Department of Mathematics, University of Maribor, PEF, Koroška 160,
2000 Maribor, Slovenia

*e-mail:* `joso.vukman@uni-mb.si`

*e-mail:* `irena.kosi@uni-mb.si`

**Abstract.** Let *R* be a 2-torsion free semiprime
ring with extended centroid *C* and let
*T* : *R*
→ *R* be an
additive mapping. Suppose that
3*T*(*xyx*) = *T*(*x*)*yx* +
*x**T*(*y*)*x* + *xy**T*(*x*)
holds for all *x,y*
∈ *R*.
Then there exists an element
λ ∈ *C* such that
*T*(*x*) =
λ *x* for all *x*
∈ *R*.

**2000 Mathematics Subject Classification.**
16N60, 39B05.

**Key words and phrases.** Prime ring, semiprime ring, derivation,
Jordan derivation, Jordan triple derivation, left (right)
centralizer, left (right) Jordan centralizer, centralizer.

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