Equations related to derivations on prime rings

Maja Fošner (Author), Joso Vukman (Author)

Abstract

In this paper we prove the following result. Let ▫$m \ge 0$▫ and ▫$n\ge 0$▫ be integers with ▫$m+n \ne 0$▫ and let ▫$R$▫ be a prime ring with ▫$char(R)=0$▫ or ▫$m+n+1 \le char(R) \ne 2$▫. Suppose there exists a nonzero additive mapping ▫$D:R \to R$▫ satisfying the relation ▫$D(x^{m+n+1}) = (m+n+1)x^m D(x)x^n$▫ for all ▫$x \in R$▫. In this case ▫$D$▫ is a derivation and ▫$R$▫ is commutative.

Keywords

matematika;prakolobar;funkcijska identiteta;odvajanje;mathematics;prime ring;functional identity;derivation;

Data

Language:	English
Year of publishing:	2011
Typology:	1.01 - Original Scientific Article
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
UDC:	512.552
COBISS:	18432520
ISSN:	0017-095X
Views:	407
Downloads:	25
Average score:	0 (0 votes)
Metadata: