Jordan derivations revisited

Abstract

Naj bo ▫$d$▫ jordansko odvajanje iz algebre ▫$\mathcal{A}$▫ v ▫$\mathcal{A}$▫-bimodul ▫$\mathcal{M}$▫. Naš glavni rezultat med drugim pove, da je zožitev ▫$d$▫ na ideal algebre ▫$\mathcal{A}$▫ generiran z določenimi višjimi komutatorji v ▫$\mathcal{A}$▫ odvajanje. S pomočjo te splošne ugotovitve se zatem ugotovi, da je ob predpostavki različnih dodatnih pogojev ▫$d$▫ nujno odvajanje na ▫$\mathcal{A}$▫. Nadalje je prikazanih več primerov pravih jordanskih odvajanj, karakterizirane so ▫$C^\ast$▫-algebre s pravimi aditivnimi jordanskimi odvajanji, in poiskana je zveza s sorodnimi problemi o jordanskih homomorfizmih in jordanskimi ▫$\mathcal{A}$▫-modulskimi homomorfizmi.

Keywords

matematika;algebra;komutator;jordansko odvajanje;odvajanje;mathematics;communitator;derivation;Jordan derivation;

Data

Language:	English
Year of publishing:	2005
Typology:	1.01 - Original Scientific Article
Organization:	UM PEF - Faculty of Education
UDC:	512.552
COBISS:	13984601
ISSN:	0305-0041
Views:	716
Downloads:	80
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Unknown
Secondary title:	Alternativni pristop k študiju jordanskih odvajanj
Secondary abstract:	Let ▫$d$▫ be a Jordan derivation from a ring ▫$\mathcal{A}$▫ into an ▫$\mathcal{A}$▫-bimodule ▫$\mathcal{M}$▫. Our main result in particular shows that the restriction of ▫$d$▫ to the ideal of ▫$\mathcal{A}$▫ generated by certain higher commutators of ▫$\mathcal{A}$▫ is a derivation. This general statement is used for proving that under various additional conditions ▫$d$▫ must be a derivation on ▫$\mathcal{A}$▫. Furthermore, several examples of proper Jordan derivations are given, ▫$C^{\ast}$▫-algebras admitting proper additive Jordan derivations are characterized, and the connections with related problems on Jordan homomorphisms and Jordan ▫$\mathcal{A}$▫-module homomorphisms are discussed.
Secondary keywords:	matematika;algebra;komutator;jordansko odvajanje;odvajanje;
Type (COBISS):	Not categorized
Pages:	str. 411-425
Volume:	ǂVol. ǂ139
Issue:	ǂPart ǂ3
Chronology:	2005
ID:	1472728