20.500.12556/DKUM-51422 Commuting and centralizing mappings in prime rings Komutirajoča in centralizirajoča preslikava na prakolobarjih 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. 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. 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 true false false Angleški jezik Angleški jezik Delo ni kategorizirano 2015-07-10 14:45:57 2015-07-10 14:45:57 2022-05-29 03:08:06 2019-07-11 07:18:34 1990 0 0 str. 47-52 no. 1 Vol. 109 1990 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.552 2335236 298524 0002-9939 URN:SI:UM:DK:ITCSXLKE http://dx.doi.org/10.1090/S0002-9939-1990-1007517-3 1 https://dk.um.si/Dokument.php?lang=slv&id=75982 Ekonomsko-poslovna fakulteta 0 0 0