20.500.12556/RUL-120125 Struktura končno razsežnih algeber delo diplomskega seminarja Structure of finite dimensional algebras Besedilo obravnava osnovne vrste kolobarjev, kot so na primer enostavni kolobarji, prakolobarji, polprakolobarji, itd. Sproti se rezultate analogno prilagaja za algebre, saj je glavni cilj besedila dokazati Wedderburnov strukturni izrek za končno razsežne algebre. Precejšen poudarek je na pojmu modula. Potreben je tako za dokaze pomembnih rezultatov, kot tudi za vpeljavo pojma primitivnega kolobarja, ki je ključen pri formulaciji Jacobsonovega izreka o gostoti, na katerem sloni dokaz Wedderburnovega strukturnega izreka. This work deals with basic types of rings, such as simple rings, prime and semiprime rings, etc. Along the way, the results are being adjusted to hold also for algebras, since the main goal of the thesis is to prove Wedderburn’s structure theorem for finite dimensional algebras. The concept of a module is emphasised in the text. It is often used when proving some of the important results, and, moreover it plays a key role in introducing the notion of a primitive ring. The latter is used in the formulation of Jacobson Density Theorem, which provides the necessary tool to prove Wedderburn’s structure theorem. algebra anihilator modula gost kolobar linearnih operatorjev vektorskega prostora nasprotni kolobar nilpotenten ideal $K$-modul polprakolobar prakolobar primitiven kolobar vektorski prostor nad obsegom algebra annihilator of a module dense ring of linear operators of a vector space ideal opposite ring nilpotent ideal $K$-module semiprime ring prime ring primitive ring vector space over a division ring true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2020-09-16 08:15:07 2020-09-16 08:15:09 2024-05-29 14:42:03 0000-00-00 00:00:00 2020 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512 110216 58838787 1474.pdf 1474.pdf 1 4B2C271BA840326FE90CE30A8E5C61BD 53f80ab0f54774eff6f143178b9e6e8af8b169010aefc7ab684b8c6f3316e643 00768cf6-a1ba-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=134880 Fakulteta za matematiko in fiziko 0 0 0