Glasnik Matematicki, Vol. 46, No.1 (2011), 31-41.

EQUATIONS RELATED TO DERIVATIONS ON PRIME RINGS

Maja Fošner and Joso Vukman

Faculty of logistics, University of Maribor, Mariborska cesta 2, 3000 Celje, Slovenia
e-mail: maja.fosner@uni-mb.si

Department of Mathematics and Computer Science, Faculty of natural sciences and mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
e-mail: joso.vukman@uni-mb.si


Dedicated to the memory of Professor Svetozar Kurepa


Abstract.   In this paper we prove the following result. Let m ≥ 0 and n ≥ 0 be integers with m+n ≠ 0 and let R be a prime ring with char(R)=0 or m+n+1 ≤ char(R) ≠ 2. Suppose there exists a nonzero additive mapping D:R → R satisfying the relation D(xm+n+1)=(m+n+1)xmD(x)xn for all x in R. In this case D is a derivation and R is commutative.

2000 Mathematics Subject Classification.   16N60, 39B05.

Key words and phrases.   Prime ring, functional identity, derivation.


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DOI: 10.3336/gm.46.1.06


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