doktorska disertacija
Benjamin Marcen (Author), Joso Vukman (Mentor), Maja Fošner (Co-mentor)

Abstract

V doktorski disertaciji si bomo v uvodu ogledali nekaj osnovnih pojmov, definicij ter pomembnejših rezultatov s področja algebre. Obravnavali bomo funkcionalne enačbe, ki so v zvezi z odvajanji, centralizatorji ter sorodnimi preslikavami na prakolobarjih, polprakolobarjih in standardnih operatorskih algebrah. Na tem področju že vrsto let delujejo tudi slovenski matematiki, ki so s svojimi rezultati pomembno vplivali na razvoj tega področja. Že v osemdesetih letih sta bila močno dejavna na tem področju J. Vukman, M. Brešar, sledili pa so B. Zalar, B. Hvala, v novejšem času pa M. Fošner, I. Kosi-Ulbl, D. Benkovič, D. Eremita, A. Fošner, N. Peršin ter N. Širovnik. Osnovno sredstvo pri reševanju funkcionalnih enačb, ki bodo predstavljene v disertaciji, je teorija funkcijskih identitet, ki jo je leta 2000 v cite {87} predstavil M. Brešar. Leta 2007 pa so jo M. Brešar, M. A. Chebotar in W. S. Martindale III tudi podrobneje predstavili v knjigi cite{MB4}. Teorija funkcijskih identitiet bo v disertaciji predstavljena skupaj s polinomskimi identitietami ter d-prostimi množicami.

Keywords

aditivna preslikava;linearni operatorji;odvajanje;jordansko odvajanje;jordansko trojno odvajanje;centralizatorji;funkcionalne enačbe;standardna operatorska algebra;prakolobarji;polprakolobarji;Banachov prostor;involucija;disertacije;

Data

Language: Slovenian
Year of publishing:
Typology: 2.08 - Doctoral Dissertation
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: B. Marcen]
UDC: 512.552(043.3)
COBISS: 22691848 Link will open in a new window
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Other data

Secondary language: English
Secondary title: Additive mappings with additional properties in (sem)prime rings and standard oprator algebras
Secondary abstract: In doctoral thesis in the preface we will introduce some basic concepts, definitions and the significant results in the field of algebra. We shall consider the functional equations related to derivations, centralizers and other similar mappings on prime rings, semi prime ring and standard operator algebras. In this area for many years operates the Slovenian mathematicians who made with their results a significant impact on the development of this area. Already in the eighties they were strongly active in this field J. Vukman, M. Brešar, followed by B. Zalar, B. Hvala and recently, M. Fošner, I Kosi-Ulbl, D. Benkovič, D. Eremita, A. Fošner, N. Peršin and N. Širovnik. Fixed asset in solving functional equations, which will be presented in the thesis, is the theory of functional identities, which was introduced by M. Brešar in the year 2000 cite {87}. In 2007, M. Brešar, M.A. Chebotar and W.S. Martindale III also presented it in the book cite {MB4}. The theory of functional identities will be presented in the thesis together with the polynomial identities and d-free sets.
Secondary keywords: additivie mapping;linear operators;derivation;Jordan derivation;Jordan triple derivation;centralizer;functional identity;standard operator algebra;prime rings;semiprime rings;Banach space;involution;dissertations;Univerzitetna in visokošolska dela;
URN: URN:SI:UM:
Type (COBISS): Doctoral dissertation
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages: XI, 180 str.
ID: 9145475