Povzetek
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.
Ključne besede
matematika;algebra;asociativni kolobarji in algebre;Banachove algebre;kolobarji;preslikave;mathematics;associative rings and algebras;prime rings;Banach algebras;identities;derivations;
Podatki
Jezik: |
Angleški jezik |
Leto izida: |
2008 |
Tipologija: |
1.01 - Izvirni znanstveni članek |
Organizacija: |
UM FNM - Fakulteta za naravoslovje in matematiko |
UDK: |
512.552 |
COBISS: |
16160776
|
ISSN: |
0420-1213 |
Št. ogledov: |
661 |
Št. prenosov: |
362 |
Ocena: |
0 (0 glasov) |
Metapodatki: |
|
Ostali podatki
Sekundarni jezik: |
Slovenski jezik |
Sekundarne ključne besede: |
matematika;algebra;asociativni kolobarji in algebre;Banachove algebre;kolobarji;preslikave; |
URN: |
URN:SI:UM: |
Vrsta dela (COBISS): |
Znanstveno delo |
Strani: |
str. [525]-530 |
Letnik: |
ǂVol. ǂ41 |
Zvezek: |
ǂno. ǂ3 |
Čas izdaje: |
2008 |
ID: |
9595926 |