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Title:Kolobar celoštevilskih kvaternionov
Authors:ID Cigler, Urška (Author)
ID Grašič, Mateja (Mentor) More about this mentor... New window
Files:.pdf MAG_Cigler_Urska_2016.pdf (292,79 KB)
MD5: 2CD54B5E428DB4F0DCB764F27ACDA2AE
 
Language:Slovenian
Work type:Master's thesis/paper
Typology:2.09 - Master's Thesis
Organization:FNM - Faculty of Natural Sciences and Mathematics
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:Kolobar, podkolobar, ideal, kolobar kvaternionov, Hurwitzov kolobar, Lagrangev izrek.
Place of publishing:Maribor
Publisher:[U. Cigler]
Year of publishing:2016
PID:20.500.12556/DKUM-60584 New window
UDC:512.71(043.2)
COBISS.SI-ID:22411016 New window
NUK URN:URN:SI:UM:DK:PPDLX4LX
Publication date in DKUM:10.08.2016
Views:1632
Downloads:121
Metadata:XML DC-XML DC-RDF
Categories:FNM
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Secondary language

Language:English
Title:The ring of integral quaternions
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.
Keywords:Ring, subring, ideal, ring of quaternions, Hurwitz ring, theorem of Lagrange.


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