On some equations in prime rings

Maja Fošner (Author), Joso Vukman (Author)

Abstract

The main purpose of this paper is to prove the following result. Let ▫$R$▫ be a prime ring of characteristic different from two and let ▫$T : R \to R$▫ be an additive mapping satisfying the relation ▫$T(x^3) = T(x)x^{2} - xT(x)x + x^{2} T(x)$▫ for all ▫$x \in R$▫. In this case ▫$T$▫ is of the form ▫$4T(x) = qx + xq$▫, where ▫$q$▫ is some fixed element from the symmetric Martindale ring of quotients. This result makes it possible to solve some functional equations in prime rings with involution which are related to bicircular projections.

Keywords

matematika;algebra;prakolobar;polprakolobar;funkcijska identiteta;odvajanje;jordansko odvajanje;involucija;bicirkularni projektor;mathematics;prime ring;semiprime ring;functional identity;derivation;Jordan derivation;involution;bicircular projection;

Data

Language:	English
Year of publishing:	2007
Typology:	1.01 - Original Scientific Article
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
UDC:	512.552
COBISS:	15609352
ISSN:	0026-9255
Views:	809
Downloads:	72
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
URN:	URN:SI:UM:
Type (COBISS):	Not categorized
Pages:	str. 135-150
Volume:	ǂVol. ǂ152
Issue:	ǂno. ǂ2
Chronology:	2007
ID:	1475130