magistrsko delo
Urška Cigler (Author), Mateja Grašič (Mentor)

Abstract

Lagrangev izrek pravi, da lahko vsako naravno število zapišemo kot vsoto štirih kvadratov. V magistrskem delu bomo to dokazali z uporabo kolobarja celoštevilskih kvaternionov, imenovanim Hurwitzov kolobar. Predstavili bomo tudi nekatere lastnosti kolobarja kvaternionov. Podrobneje pa se bomo posvetili še posebnemu podkolobarju kolobarja kvaternionov - Hurwitzovemu kolobarju.

Keywords

kolobarji;podkolobarji;ideali;kolobarji kvaternionov;Hurwitzov kolobar;Lagrangev izrek;magistrska dela;

Data

Language: Slovenian
Year of publishing:
Typology: 2.09 - Master's Thesis
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: [U. Cigler]
UDC: 512.71(043.2)
COBISS: 22411016 Link will open in a new window
Views: 851
Downloads: 85
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Other data

Secondary language: English
Secondary title: The ring of integral quaternions
Secondary abstract: Classical theorem of Lagrange states that every positive integer can be expressed as a sum of squares of four integers. In this dissertation, we will prove this theroem using the ring of integral quaternions known as the ring of Hurwitz integral quaternions. We will also present some of the basic properties of the ring of quaternions and its subring of integral quaternions, the Hurwitz ring of integral quaternions.
Secondary keywords: rings;subrings;ideals;rings of quaternions;Hurwitz ring;theorem of Lagrange;master theses;
Type (COBISS): Master's thesis/paper
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages: 27 f.
ID: 9151917