Glasnik matematički, Vol. 46 No. 1, 2011.
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
Publication date:
13.6.2011.
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