delo diplomskega seminarja
Nik Erzetič (Author), Matej Brešar (Mentor)

Abstract

Najprej se seznanimo z osnovnimi pojmi, kot so kolobar in modul. Pripravimo nekaj izrekov, s katerimi bomo dokazali osnovni izrek - med njimi je kitajski izrek o ostankih za kolobarje. Nato dokažemo dve obliki osnovnega izreka o končno generiranih modulih nad glavnimi kolobarji. Na koncu osnovni izrek za module uporabimo za dokaz osnovnega izreka o končno generiranih Abelovih grupah in dokaz obstoja Jordanove kanonične forme matrike.

Keywords

matematika;moduli;glavni kolobarji;osnovni izreki;Jordanova kanonična forma;

Data

Language: Slovenian
Year of publishing:
Typology: 2.11 - Undergraduate Thesis
Organization: UL FMF - Faculty of Mathematics and Physics
Publisher: [N. Erzetič]
UDC: 512
COBISS: 79890435 Link will open in a new window
Views: 728
Downloads: 49
Average score: 0 (0 votes)
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Other data

Secondary language: English
Secondary title: Modules over PIDs and their applications
Secondary abstract: First, we present the basic definition, such as that of a ring and a module. We construct a number of theorems needed in proof of the fundamental theorem, including the Chineese remained theorem for rings. Next, we prove two forms of the fundamental theorem of finitely generated modules over PID. Lastly, we employ the module fundamental theorem to prove the fundamental theorem of finitely generated Abelian groups and the existance of the Jordan normal matrix form.
Secondary keywords: mathematics;module;PID;principal ideal domain;fundamental theorems;Jordan normal form;
Type (COBISS): Final seminar paper
Study programme: 0
Thesis comment: Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages: 27 str.
ID: 13668080
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