20.500.12556/DKUM-60584 Kolobar celoštevilskih kvaternionov The ring of integral quaternions 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. 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. Kolobar podkolobar ideal kolobar kvaternionov Hurwitzov kolobar Lagrangev izrek. Ring subring ideal ring of quaternions Hurwitz ring theorem of Lagrange. true true false [U. Cigler] Slovenski jezik Angleški jezik Magistrsko delo/naloga 2016-06-25 20:22:06 2016-08-10 12:54:18 2022-06-23 03:11:28 2019-07-11 11:51:23 2016 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.71(043.2) 22411016 URN:SI:UM:DK:PPDLX4LX MAG_Cigler_Urska_2016.pdf MAG_Cigler_Urska_2016.pdf 1 2CD54B5E428DB4F0DCB764F27ACDA2AE 3d8344a4b390951a84c47fec99e57da97473122d25cabbcf3f15b634e4217410 c83cdc5f-7c0c-11eb-bb7a-00155d0001ca https://dk.um.si/Dokument.php?lang=slv&id=95449 Fakulteta za naravoslovje in matematiko 0 0 0