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

EQUATIONS RELATED TO DERIVATIONS ON PRIME RINGS

Maja Fošner and Joso Vukman

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(x^m+n+1)=(m+n+1)x^mD(x)xⁿ for all x 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.

DOI: 10.3336/gm.46.1.06

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