Symmetric bi-derivations on prime and semi-prime rings

Abstract

Naj bo ▫$K$▫ kolobar. Biaditivna simetrična preslikava ▫$D(.,.):K \times K \to K$▫ je simetrična biderivacija, če je za vsak fiksen ▫$y \in K$▫ preslikava ▫$x \mapsto D(x,y)$▫ derivacija. Glavni namen članka je dokazati rezultat v smislu klasičnega izreka E. Posnerja, ki pravi naslednje: Če je ▫$K$▫ prakolobar s karakteristiko različno od dva in sta ▫$D_1$▫ in ▫$D_2$▫ od nič različni derivaciji, potem preslikava ▫$x \mapsto D_1(D_2(x))$▫ ne more biti derivacija.

Keywords

matematika;asociativni kolobarji in algebre;kolobar;prakolobar;polprakolobar;derivacija;simetrična biderivacija;mathematics;associative rings and algebras;prime ring;semiprime ring;derivation;simetric biderivation;Banach algebra;

Data

Language:	English
Year of publishing:	1989
Typology:	1.01 - Original Scientific Article
Organization:	UM EPF - Faculty of Economics and Business
UDC:	512.552
COBISS:	1332228
ISSN:	0001-9054
Views:	882
Downloads:	85
Average score:	0 (0 votes)
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Other data

Secondary language:	English
Secondary title:	Simetrične biderivacije na prakolobarjih in polprakolobarjih
Secondary abstract:	Let ▫$R$▫ be a ring. A biadditive symmetric mapping ▫$D(.,.):R \times R \to R$▫ is called a symmetric bi-derivation if, for any fixed ▫$y \in R$▫, a mapping ▫$x \mapsto D(x,y)$▫ is a derivation. The purpose of this paper is to prove some results concerning symmetric bi-derivations on prime and semi-prime rings. We prove that existence of a nonzero symmetric bi-derivation ▫$D(.,.): R\times R \to R$▫ where ▫$R$▫ is a prime ring of characteristic not two, with the property ▫$D(x,x)x = xD(x,x), \; x \in R$▫, forces ▫$R$▫ to be commutative. A theorem in the spirit of a classical result first proved by E. Posner, which states that, if ▫$R$▫ is a prime ring of characteristic not two and ▫$D_1$▫, ▫$D_2$▫ are nonzero derivations on ▫$R$▫, then the mapping ▫$x \mapsto D_1(D_2(x))$▫ cannot be a derivation, is also presented.
URN:	URN:SI:UM:
Type (COBISS):	Not categorized
Pages:	str. 245-254
Volume:	ǂVol. ǂ38
Issue:	ǂiss. ǂ2-3
Chronology:	1989
ID:	1471761