Some results concerning additive mappings and derivations on semiprime rings

Ajda Fošner (Author), Joso Vukman (Author)

Abstract

Naj bo ▫$R$▫ polprakolobar in ▫$f \colon R \to R$▫ aditivna preslikava, ki zadošča ▫$[f(x),x^2] = 0$▫ za vse ▫$x \in R$▫. V članku je dokazano, da je potem ▫$[f(x),x] = 0$▫ za vse ▫$x \in R$▫. S pomočjo tega rezultata lahko dokažemo naslednje. Naj bo ▫$R$▫ polprakolobar in ▫$D,G \colon R \to R$▫ odvajanji. Predpostavimo, da je ▫$[D^2(x) + G(x),x^2] = 0$▫ za vse ▫$x \in R$▫. Potem ▫$D$▫ in ▫$G$▫ slikata ▫$R$▫ v njegov center.

Keywords

algebra;prakolobar;polprakolobar;odvajanje;centralizirajoče preslikave;komutirajoče preslikave;poševno-komutirajoča preslikava;prime ring;semiprime ring;derivation;centralizing mapping;commuting mapping;skew-commuting mapping;

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:	15884633
ISSN:	0033-3883
Views:	66
Downloads:	5
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary title:	Nekaj rezultatov o aditivnih preslikavah in odvajanjih na polprakolobarjih
Secondary abstract:	Let ▫$R$▫ be a 2-torsion free semiprime ring and let ▫$f \colon R \to R$▫ be an additive mapping satisfying the relation ▫$[f(x),x^2] = 0$▫ for all ▫$x \in R$▫. We prove that in this case ▫$[f(x),x] = 0$▫ holds for all ▫$x \in R$▫. This result makes it possible to prove the following result. Let ▫$R$▫ be a 2-torsion free semiprime ring and let ▫$D,G \colon R \to R$▫ be derivations. Suppose that the relation ▫$[D^2(x) + G(x),x^2] = 0$▫ holds for all ▫$x \in R$▫. Then ▫$D$▫ and ▫$G$▫ both map $R$ into its center.
Secondary keywords:	algebra;prakolobar;polprakolobar;odvajanje;centralizirajoče preslikave;komutirajoče preslikave;poševno-komutirajoča preslikava;
Type (COBISS):	Not categorized
Pages:	str. 575-581
Volume:	ǂVol. ǂ78
Issue:	ǂno. ǂ3-4
Chronology:	2011
ID:	8723759