prikaz prve stranice dokumenta Algebarska proširenja polja
  Download
PDF 283.38 KB
master's thesis
Algebarska proširenja polja
Zagreb: University of Zagreb, Faculty of Science, 2015. urn:nbn:hr:217:571422
Borovec, Elizabeta
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Borovec, E. (2015). Algebarska proširenja polja (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:571422

Borovec, Elizabeta. "Algebarska proširenja polja." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:571422

Borovec, Elizabeta. "Algebarska proširenja polja." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:571422

Borovec, E. (2015). 'Algebarska proširenja polja', Master's thesis, University of Zagreb, Faculty of Science, accessed 04 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:571422

Borovec E. Algebarska proširenja polja [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2015 [cited 2024 November 04] Available at: https://urn.nsk.hr/urn:nbn:hr:217:571422

E. Borovec, "Algebarska proširenja polja", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:217:571422

Metadata
TitleAlgebarska proširenja polja
AuthorElizabeta Borovec
MentorDražen Adamović (mentor)
Committee memberDražen Adamović (predsjednik povjerenstva)
Committee memberMarko Tadić (član povjerenstva)
Committee memberMirko Primc (član povjerenstva)
Committee memberOzren Perše (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2015-09-23, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom diplomskom radu iznijeli smo osnovne rezultate o algebarskim proširenjima polja. Definirali smo algebarska i transcendentna proširenja polja te smo proučavali konačna proširenja polja. Budući da smo definirali proširenja polja, prirodno se nameće pitanje postojanja algebarski zatvorenih polja. Dokazali smo postojanje algebarskog zatvarača za svako polje te da je algebarski zatvarač prebrojivog polja također prebrojiv. Osim toga, dokazali smo da su bilo koja dva algebarska zatvarača polja izomorfna s obzirom na definirano preslikavanje. Podijelili smo vrste polja i s obzirom na njihovu karakteristiku te smo definirali konačno polje i njegovu karakteristiku. Dokazali smo Galoisov teorem koji je važan teorem o konačnim poljima te iskazujemo i dokazujemo kada su bilo koja dva konačna polja izomorfna.
Abstract (english)
In this thesis we presented the main results of the algebraic field extensions. We have defined algebraic and transcendental extension fields and studied finite extension fields. Since we defined extension fields, naturally raises the question of the existence of algebraic closed fields. We have proven the existence of algebraic closure of each field and that algebraic closure of countable field is also countable. In addition, we showed that any two algebraic closures fields are isomorphic with respect to the defined mapping. We have divided the field types with respect to their characteristics and defined a finite field and its characteristics. We have proved Galois theorem which is an important theorem on finite fields and stated and proved, when are two finite fields isomorphic.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:571422
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2017-06-07 11:33:49