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master's thesis
Galoisova teorija
Zagreb: University of Zagreb, Faculty of Science, 2016. urn:nbn:hr:217:872806
Topić, Dragutina
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Topić, D. (2016). Galoisova teorija (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:872806

Topić, Dragutina. "Galoisova teorija." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:872806

Topić, Dragutina. "Galoisova teorija." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:872806

Topić, D. (2016). 'Galoisova teorija', Master's thesis, University of Zagreb, Faculty of Science, accessed 26 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:872806

Topić D. Galoisova teorija [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2016 [cited 2024 November 26] Available at: https://urn.nsk.hr/urn:nbn:hr:217:872806

D. Topić, "Galoisova teorija", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:217:872806

Metadata
TitleGaloisova teorija
AuthorDragutina Topić
MentorOzren Perše (mentor)
Committee memberOzren Perše (predsjednik povjerenstva)
Committee memberZvonimir Tutek (član povjerenstva)
Committee memberIlja Gogić (član povjerenstva)
Committee memberDražen Adamović (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2016-11-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Ovaj diplomski rad smo podijelili u dva dijela. U prvom dijelu smo dali kratki podsjetnik na teoriju grupa, Lagrangeov teorem, kvocijentne skupove, te komutativne prstene, polja razlomaka, te polinome. Uvodni dio nam je bio od velike važnosti kasnije za shvaćanje same Galoisove teorije. U drugom dijelu smo se upoznali s Galoisovom teorijom, čiji je originalni naziv teorija jednadžbi. Odmah na početku smo definirali Galoisovu grupu. Sama Galoisova teorija nam daje vezu između algebarskog proširenja \(E\) nad poljem \(k\), te pripadne Galoisove grupe \(Gal(E/k)\). Naveli smo nekoliko teorema o Galoisovim grupama čije tvrdnje kažu da su proširenja polja također i polja razlaganja nekog polinoma. Na samom kraju smo iskazali i dokazali Fundamentalni teorem Galoisove teorije, kao posljedicu cjelokupne analize drugog dijela.
Abstract (english)
This thesis is divided into two parts. The first part was a brief reminder of the group theory, Lagrange’s theorem, quotient groups, and commutative rings, fields fractions, and polynomials. The introductory part was of great importance for the understanding of Galois theory in the second part. In the second part, we got familiar with Galois theory, which original name was the theory of equations. Right at the beginning we defined the Galois group. Galois theory gives connection between algebraic extension \(E\) over the field \(k\), and the corresponding Galois group \(Gal(E/k)\). We stated some theorems about Galois groups which say that an extension is a splitting field of a polynomial. At the very end we stated and proved the fundamental theorem of Galois theory, as a result of the overall analysis of the second part.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:872806
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 on2017-03-29 12:53:12