On some functional equations arising from (m, n)-Jordan derivations and commutativity of prime rings

Maja Fošner (Author), Joso Vukman (Author)

Abstract

The purpose of this paper is to prove the following result. Let ▫$m, n \ge 1$▫ be some fixed integers with ▫$m \ne n$▫, and let ▫$R$▫ be a prime ring with ▫$(m+n)^2 < \text{char} (R)$▫. Suppose a nonzero additive mapping ▫$D : R \to R$▫ exists satisfying the relation ▫$(m+n)^2 D(x^3) = m(3m+n) D(x)x^2 + 4mnxD(x)x + n(3n+m)x^2 D(x)$▫ for all ▫$x \in R$▫. In this case ▫$D$▫ is a derivation and ▫$R$▫ is commutative.

Keywords

matematika;prakolobar;polprakolobar;odvajanje;jordansko odvajanje;levo odvajanje;mathematics;prime ring;semiprime ring;derivation;Jordan derivation;left dderivation;left Jordan derivation;(m, n)-Jordan drivation;

Data

Language:	English
Year of publishing:	2012
Typology:	1.01 - Original Scientific Article
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
UDC:	512.552.3
COBISS:	19371016
ISSN:	0035-7596
Views:	354
Downloads:	28
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
URN:	URN:SI:UM:
Type (COBISS):	Not categorized
Pages:	str. 1153-1168
Volume:	Vol. 42
Issue:	no. 4
Chronology:	2012
ID:	1477046