ǂAn ǂidentity with derivations on rings and Banach algebras

Ajda Fošner (Author), Maja Fošner (Author), Joso Vukman (Author)

Abstract

The main purpose of this paper is to study the following: Let m, n, and ▫$k_{i}, i = 1, 2, ..., n$▫ be positive integers and let ▫$R$▫ be a ▫$2m(m+ k_{1} + k_{2} + ... + k_{n} -1)!$▫-torsion free semiprime ring. Suppose that there exist derivations ▫$D_{i} : R \to R, i = 1, 2, ..., n + 1$▫ , such that ▫$D_{1}(x^{m})x^{k_{1}+...+k_{n}}+x^{k_{1}} D_{2}(x^{m})x^{k_{2}+...+k_{n}}+...+x^{k_{1}+...+k_{n}}D_{n+1}(x^{m})=0$▫ holds for all ▫$x \in R$▫. Then we prove that ▫$D_{1}+D_{2}+...+D_{n+1}=0$▫ and that the derivation ▫$k_{1}D_{2}+(k_{1}+k_{2})D_{3}+...+(k_{1}+k_{2}+...+k{n})D_{n+1}$▫ maps ▫$R$▫ into its center. We also obtain a range inclusion result of continuous derivations on Banach algebras.

Keywords

matematika;algebra;asociativni kolobarji in algebre;Banachove algebre;kolobarji;preslikave;ne zaključna dela;mathematics;associative rings and algebras;prime rings;Banach algebras;identities;derivations;

Data

Language:	English
Year of publishing:	2008
Typology:	1.01 - Original Scientific Article
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	De Gruyter Brill
UDC:	512.552
COBISS:	16160776
ISSN:	0420-1213
Views:	1388
Downloads:	476
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary keywords:	Algebra;Linearni operatorji;
URN:	URN:SI:UM:
Type (COBISS):	Scientific work
Pages:	str. [525]-530
Volume:	ǂVol. ǂ41
Issue:	ǂno. ǂ3
Chronology:	2008
ID:	9595926