Aditivne preslikave z dodatnimi lastnostmi na (pol)prakolobarjih in standardnih operatorskih algebrah - Marcen, Benjamin (visokošolska dela, 2016)
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.
Keywords: additivie mapping; aditivna preslikava; Algebra; Banach space; Banachov prostor; centralizatorji; centralizer; derivation; Disertacije; dissertations; functional identity; funkcionalne enačbe; involucija; involution; Jordan derivation; Jordan triple derivation; jordansko odvajanje; jordansko trojno odvajanje; linear operators; linearni operatorji; odvajanje; polprakolobarji; prakolobarji; prime rings; semiprime rings; standard operator algebra; standardna operatorska algebra