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master's thesis
Matrice nad nekomutativnim prstenima
Zagreb: University of Zagreb, Faculty of Science, 2016. urn:nbn:hr:217:401558
Fijan, Lucija
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Fijan, L. (2016). Matrice nad nekomutativnim prstenima (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:401558

Fijan, Lucija. "Matrice nad nekomutativnim prstenima." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:401558

Fijan, Lucija. "Matrice nad nekomutativnim prstenima." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:401558

Fijan, L. (2016). 'Matrice nad nekomutativnim prstenima', Master's thesis, University of Zagreb, Faculty of Science, accessed 26 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:401558

Fijan L. Matrice nad nekomutativnim prstenima [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2016 [cited 2024 November 26] Available at: https://urn.nsk.hr/urn:nbn:hr:217:401558

L. Fijan, "Matrice nad nekomutativnim prstenima", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:217:401558

Metadata
TitleMatrice nad nekomutativnim prstenima
AuthorLucija Fijan
MentorOzren Perše (mentor)
Committee memberOzren Perše (predsjednik povjerenstva)
Committee memberMarcela Hanzer (član povjerenstva)
Committee memberPavle Pandžić (član povjerenstva)
Committee memberGoran Muić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2016-09-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Tema ovog radu su matrice nad nekomutativnim prstenom. U prvom i drugom poglavlju pod nazivom Prsteni i Moduli uvodimo osnovne pojmove koji su nam potrebni u daljnjem dijelu rada. Pojam poluprostota, kojim se bavimo u trećem poglavlju, je najosnovniji termin koji se proteze kroz čitav diplomski rad. Prezentiramo tri definicije poluprostog modula i dokazujemo da su one ekvivalentne. Pomoću navedenih uvjeta možemo dokazati Jacobsonov teorem o gustoći te definirati pojmove poluprostog i prostog prstena. Uz Jacobsonov teorem u radu dokazujemo i druge važne teoreme, kao primjer Wedderburnov teorem koji nam daje prikaz prstena R kao D-endomorfizam nad modulom E, gdje sa D označavamo konačnodimenzionalnu algebru sa dijeljenjem nad poljem k.
Abstract (english)
The theme of this paper are matrices over noncommutative ring. In the first and second chapter titled Rings and Modules we introduce the basic concepts that are required in the far part of the work. The concept semisimplicity, the main theme of the third chapter, is the most basic term that runs through this entire graduate paper. We present three definitions of semisimple modules and prove that they are equivalent. Besides Jacobson’s theorem we also prove some others very important theorems, for example Wedderbun’s theorem which gives us a representation of a ring R as the ring of D-endomorphisms of module E, where D is a finite-dimensional division algebra over a field k. Using the above conditions we can prove Jacobson’s density theorem and define the terms of semisimple and simple ring.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:401558
Study programmeTitle: Applied Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-01-22 10:08:18