diplomsko delo
Ana Marija Varšnik (Author), Maja Fošner (Mentor)

Abstract

Diplomsko delo z naslovom Nekateri rezultati o odvajanjih na prakolobarjih je razdeljeno na dve poglavji. Prvo poglavje je namenjeno osnovnim pojmom, ki jih potrebujemo za razumevanje diplomskega dela. V podrazdelkih smo se osredotočili, med drugim, na pojme grupa, kolobar, ideal, algebra, prakolobar, polprakolobar, odvajanje in Jordansko odvajanje. V drugem poglavju, ki je cilj diplomskega dela, bodo predstavljeni izreki in dokazi, ki jih potrebujemo za dokaz klasičnega rezultata I. N.Hersteina, ki pravi, da je vsako Jordansko odvajanje na prakolobarju s karakteristiko različno od dva odvajanje. Prav tako bomo zapisali Posnerjev izrek, ki pravi, da produkt dveh neničelnih odvajanj na prakolobarju, s karakteristiko različno od dva, ni odvajanje.

Keywords

diplomska dela;kolobarji;grupe;prakolobarji;polprakolobarji;ideal;algebra;odvajanje;Jordansko odvajanje;

Data

Language: Slovenian
Year of publishing:
Typology: 2.11 - Undergraduate Thesis
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: [A. M. Varšnik]
UDC: 512.552.3(043.2)
COBISS: 22477320 Link will open in a new window
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Other data

Secondary language: English
Secondary title: Some results on derivations in prime rings
Secondary abstract: In the Graduation Thesis with the title Some results on derivations in prime rings, we will first introduce the basicterminology. We will present some definitions, such as group, ring, ideal, algebra, prime ring, semi prime ring, derivation, Jordan derivation. In the second part of the Thesis we will focus on theorems and proofs, which we need for proving classical result of I. N. Herstein. He proved that every Jordan derivation in prime ring of characteristics not two is also a derivation. We will present Posner theorem which defines that product of two non zero derivations in prime ring of characteristics not two is not a derivation.
Secondary keywords: theses;rings;groups;prime rings;semi prime rings;ideal;algebra;derivation;Jordan derivation;
URN: URN:SI:UM:
Type (COBISS): Undergraduate thesis
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages: IX, 31 f.
ID: 9155186