Original scientific paper

Equations related to derivations on prime rings

Maja Fošner ; Faculty of logistics, University of Maribor, Mariborska cesta 2, 3000 Celje, Slovenia
Joso Vukman ; Department of Mathematics and Computer Science, Faculty of natural sciences and mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia

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 R. In this case D is a derivation and R is commutative.

Keywords

Prime ring; functional identity; derivation

Hrčak ID:

68869

URI

https://hrcak.srce.hr/68869

Publication date:

13.6.2011.

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