20.500.12556/DKUM-59739 Aditivne preslikave z dodatnimi lastnostmi na (pol)prakolobarjih in standardnih operatorskih algebrah Additive mappings with additional properties in (sem)prime rings and standard oprator algebras 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. 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. Aditivna preslikava linearen operator odvajanje jordansko odvajanje jordansko trojno odvajanje centralizator funkcionalna enačba standardna operatorska algebra prakolobar polprakolobar Banachov prostor involucija. Additive mapping linear operator derivation Jordan derivation Jordan triple derivation centralizer functional identity standard operator algebra prime ring semiprime ring Banach space involution. true true false B. Marcen] Slovenski jezik Angleški jezik Doktorsko delo/naloga 2016-05-26 13:41:07 2016-10-21 14:11:04 2023-10-12 09:04:28 2019-07-11 11:23:52 2016 0 [Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.552(043.3) 22691848 URN:SI:UM:DK:RANSAHRS DOK_Marcen_Benjamin_2016.pdf DOK_Marcen_Benjamin_2016.pdf 1 3B841915DAD12D41AB7846F3812EBC6F 270f28637c68c60f580be33ae1a289d5a14e59af8a5bb8d0b8bc1b34fbda90ae c72e70d8-7c0d-11eb-bb7a-00155d0001ca https://dk.um.si/Dokument.php?lang=slv&id=107518 Fakulteta za naravoslovje in matematiko 0 0 0