On [(m, n)]-Jordan derivations and commutativity of prime rings

Abstract

The purpose of this paper is to prove the following result. Let ▫$ m\geq\ge 1$▫, ▫$n \geq\ge 1$▫ be some fixed integers with ▫$m \ne n$▫, and let R be a prime ring with ▫$char (R) \ne 2mn (m+n) l, \vert m-n l, \vert$▫. Suppose there exists a nonzero additive mapping ▫$D : R \to R$▫ satisfying the relation ▫$(m + n)D(x^2) = 2mD(x)x + 2nxD(x)$▫ for all ▫$x \in R ((m,n)-Jordan derivation)$▫. If either ▫$char(R) = 0$▫ or ▫$char(R) \geq 3$▫ then D is a derivation and R is commutative.

Keywords

matematika;odvodi;kolobarji;jordanska odvajanja;prime rings;derivation;Jordan derivation;commutativity;

Data

Language:	English
Year of publishing:	2008
Typology:	1.01 - Original Scientific Article
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
UDC:	517.2
COBISS:	16481032
ISSN:	0420-1213
Views:	737
Downloads:	403
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary keywords:	matematika;odvodi;kolobarji;jordanska odvajanja;
URN:	URN:SI:UM:
Type (COBISS):	Scientific work
Pages:	str. 773-778
Volume:	ǂVol. ǂ41
Issue:	ǂno. ǂ4
Chronology:	2008
ID:	9595927