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Kommutativitet i en Ore-utvidgning över en polynomring
Mälardalen University, School of Education, Culture and Communication.
2019 (Swedish)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [sv]

I denna uppsats studerar vi kommutativitet i polynomringar i en variabel med icke-kommutativ multiplikation över en domän, så kallade Ore-utvidgningar. Vi Ore-utvidgar en polynomring i en variabel med koefficienter tillhörande en kropp. Vi studerar centralisatorer i denna Ore-utvidgning. Centralisatorn av ett icke-konstant element visar sig vara kommutativa och fria moduler. Vi undersöker även när centralisatorerna som en algebra är genererade av ett element. Några nya exempel av sådana centralisatorer presenteras. Vi undersöker också en ny metod för att bestämma om centralisatorn som en algebra är genererad av ett element.

Abstract [en]

In this thesis, we study commutativity in polynomial rings in one variable with noncommutative multiplication over a domain, which is called Ore extensions. We look at the Ore extension of a polynomial ring in one variable with coefficients belonging to a field. We study centralizers in this Ore extension. The centralizer of a nonconstant element turns out to be commutative and a free module. We also investigate when the centralizers as an algebra are generated by one element. Some new examples of such centralizers are presented. We also look into a new method to determine if the centralizers as an algebra are generated by one element.

Place, publisher, year, edition, pages
2019. , p. 29
Keywords [en]
Ore extension
Keywords [sv]
Ore-utvidgning, polynomring, ringteori, algebra, kommutativitet, ring
National Category
Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-43592OAI: oai:DiVA.org:mdh-43592DiVA, id: diva2:1319985
Subject / course
Mathematics/Applied Mathematics
Supervisors
Examiners
Available from: 2019-06-10 Created: 2019-06-03 Last updated: 2019-06-10Bibliographically approved

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kandidatKlinga(243 kB)13 downloads
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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf