Odvajanja na kolobarjih in operatorskih algebrah

diplomsko delo

Nejc Širovnik (Author), Joso Vukman (Mentor)

Abstract

V prvem delu diplomskega dela se seznanimo s strukturama prakolobar in pol prakolobar. Na kolobarju vpeljemo pojme odvajanje, jordansko odvajanje in jordansko trojno odvajanje. I. N. Herstein je leta 1957 dokazal, da je na prakolobarju brez elementov reda dva vsako jordansko odvajanje tudi odvajanje. V diplomskem delu je predstavljen alternativni dokaz tega izreka, ki sta ga leta 1988 objavila M. Brešar in J. Vukman. J. Cusack je leta 1975 Hersteinov izrek posplošil na pol prakolobarje brez elementov reda dva. V diplomskem delu je predstavljen dokaz tega izreka, ki ga je leta 1988 objavil M. Brešar. M. Brešar je leta 1989 dokazal, da je vsako jordansko trojno odvajanje na pol prakolobarju brez elementov reda dva tudi odvajanje. V diplomskem delu najdemo dokaz tega izreka s krepkejšimi predpostavkami. Predstavljena sta tudi nova rezultata, ki spominjata na prej omenjen Brešarjev rezultat. Drugi del diplomskega dela sega na področje funkcionalne analize. Osnova je rezultat P. R. Chernoffa, ki govori o linearnih odvajanjih na standardnih operatorskih algebrah realnega ali kompleksnega Banachovega prostora. Predstavljene so različne posplošitve tega rezultata.

Keywords

matematika;kolobarji;odvajanja;prakolobarji;operatorska algebra;jordansko odvajanje;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2010
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[N. Širovnik]
UDC:	51(043.2)
COBISS:	17854216
Views:	2377
Downloads:	174
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	DERIVATIONS ON RINGS AND OPERATOR ALGEBRAS
Secondary abstract:	The first part of the Graduation Thesis introduces prime and semiprime rings. On arbitrary ring concepts as derivation, Jordan derivation and Jordan triple derivation are defined. In year 1957 I. N. Herstein proved that every Jordan derivation on 2-torsion free prime ring is also a derivation. In the Thesis we present the alternative proof of this theorem, which was published by M. Brešar and J. Vukman in 1988. In year 1975 J. Cusack generalized Herstein's theorem on 2-torsion free semiprime rings. We present the proof of this theorem, which was published by M. Brešar in 1988. One year later he also proved that every Jordan triple derivation on 2-torsion free semiprime ring is a derivation as well. In the Thesis we present the proof of this theorem with some stronger assumptions. At the end of the first part two new results, motivated by Brešar's theorem, are proved. In the second part of the Thesis some results from functional analysis are proved. We present a classical result of P. R. Chernoff, concerning linear derivations on standard operator algebras of real or complex Banach space. We also meet some generalizations of Chernoff's result.
Secondary keywords:	Univerzitetna in visokošolska dela;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	39 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	18769