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master's thesis
Konačnodimenzionalne algebre s dijeljenjem
Zagreb: University of Zagreb, Faculty of Science, 2019. urn:nbn:hr:217:339404
Dević, Petar
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Dević, P. (2019). Konačnodimenzionalne algebre s dijeljenjem (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:339404

Dević, Petar. "Konačnodimenzionalne algebre s dijeljenjem." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:339404

Dević, Petar. "Konačnodimenzionalne algebre s dijeljenjem." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:339404

Dević, P. (2019). 'Konačnodimenzionalne algebre s dijeljenjem', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:339404

Dević P. Konačnodimenzionalne algebre s dijeljenjem [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2019 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:339404

P. Dević, "Konačnodimenzionalne algebre s dijeljenjem", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:217:339404

Metadata
TitleKonačnodimenzionalne algebre s dijeljenjem
AuthorPetar Dević
MentorIlja Gogić (mentor)
Committee memberIlja Gogić (predsjednik povjerenstva)
Committee memberIvan Kupčić (član povjerenstva)
Committee memberRudi Mrazović (član povjerenstva)
Committee memberVjeran Hari (član povjerenstva)
Committee memberMatko Milin (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2019-07-15, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu proučavamo neka osnovna svojstva konačnodimenzionalnih algebri s dijeljenjem. Najprije dokazujemo slavni Frobeniusov teorem, koji kaže da (do na izomorfizam) postoje točno tri realne konačnodimenzionalne algebre s dijeljenjem: Realni brojevi \(\mathbb{R}\), kompleksni brojevi \(\mathbb{C}\) te kvaternioni \(\mathbb{H}\). Nadalje, dokazujemo Wedderburnov strukturalni teorem koji opisuje strukturu konačnodimenzionalnih poluprostih algebri; svaka takva algebra je izomorfna konačnom direktnom produktu matričnih algebri nad algebrama s dijeljenjem. Time se većina pitanja vezana uz konačnodimenzionalne poluproste algebre reducira na analogna pitanja vezana uz konačnodimenzionalne algebre s dijeljenjem.
Abstract (english)
In this thesis we explore some basic properties of finite dimensional division algebras. We first present the proof of the celebrated Frobenius theorem, which states that (up to an isomorphism) there exist precisely three real finite-dimensional division algebras: Real numbers \(\mathbb{R}\), complex numbers \(\mathbb{C}\) and quaternions \(\mathbb{H}\). Next, we present the proof of the Wedderburn’s structure theorem which describes the structure of semisimple finitedimensional algebras; any such algebra is isomorphic to a finite direct product of matrix algebras over some division algebras. In this way most questions concerning semisimple finite-dimensional algebras are reduced to the analogues questions for finite-dimensional division algebras.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:339404
Study programmeTitle: Mathematics and Physics Education; specializations in: Mathematics and Physics Education
Course: Mathematics and Physics Education
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra edukacije matematike i fizike (magistar/magistra edukacije matematike i fizike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-09-25 08:56:38