Commuting and centralizing mappings in prime rings

Abstract

Naj bo ▫$R$▫ kolobar. Preslikava ▫$F: R \to R$▫ je komutirajoča na ▫$R$▫, če je ▫$[ F(x),x] = 0$▫ za vsak ▫$x \in R$▫. Glavni rezultat: naj bo ▫$R$▫ prakolobar s karakteristiko različno od dva. Denimo, da obstaja od nič različna derivacija ▫$D: R \to R$▫, pri kateri je preslikava ▫$x \mapsto [ D(x),x]$▫, komutirajoča na ▫$R$▫. V tem primeru je ▫$R$▫ komutativen.

Keywords

matematika;asociativni kolobarji in algebre;kolobar;prakolobar;odvajanje;jordansko odvajanje;notranje odvajanje;komutirajoča preslikava;centralizirajoča preslikava;mathematics;associative rings and algebras;prime ring;derivation;Jordan derivation;inner derivation;commuting mapping;centralizing mapping;

Data

Language:	English
Year of publishing:	1990
Typology:	1.01 - Original Scientific Article
Organization:	UM EPF - Faculty of Economics and Business
UDC:	512.552
COBISS:	298524
ISSN:	0002-9939
Views:	921
Downloads:	95
Average score:	0 (0 votes)
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Other data

Secondary language:	English
Secondary title:	Komutirajoča in centralizirajoča preslikava na prakolobarjih
Secondary abstract:	Let ▫$R$▫ be a ring. A mapping ▫$F: R \to R$▫ is said to be commuting on ▫$R$▫ if ▫$[F(x),x] = 0$▫ holds for all ▫$x \in R$▫. The main purpose of this paper is to prove the following result, which generalizes a classical result of E. Posner: Let ▫$R$▫ be a prime ring of characteristic not two. Suppose there exists a nonzero derivation ▫$D: R \to R$▫, such that the mapping ▫$x \mapsto [D(x),x]$▫ is commuting on ▫$R$▫. In this case ▫$R$▫ is commutative.
URN:	URN:SI:UM:
Type (COBISS):	Not categorized
Pages:	str. 47-52
Volume:	ǂVol. ǂ109
Issue:	ǂno. ǂ1
Chronology:	1990
ID:	1471745