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master's thesis
Upotpunjenja uređenih polja
Zagreb: University of Zagreb, Faculty of Science, 2021. urn:nbn:hr:217:082688
Pedić, Barbara
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Pedić, B. (2021). Upotpunjenja uređenih polja (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:082688

Pedić, Barbara. "Upotpunjenja uređenih polja." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:082688

Pedić, Barbara. "Upotpunjenja uređenih polja." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:082688

Pedić, B. (2021). 'Upotpunjenja uređenih polja', Master's thesis, University of Zagreb, Faculty of Science, accessed 30 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:082688

Pedić B. Upotpunjenja uređenih polja [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2021 [cited 2024 November 30] Available at: https://urn.nsk.hr/urn:nbn:hr:217:082688

B. Pedić, "Upotpunjenja uređenih polja", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:217:082688

Metadata
TitleUpotpunjenja uređenih polja
Title (english)Completions of edited fields
AuthorBarbara Pedić
MentorZvonko Iljazović (mentor)
Committee memberZvonko Iljazović (predsjednik povjerenstva)
Committee memberFranka Miriam Brückler (član povjerenstva)
Committee memberŽeljka Milin Šipuš (član povjerenstva)
Committee memberMarko Erceg (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2021-03-04, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom diplomskom radu, kroz prvo poglavlje proučavani su pojmovi uređene grupe, uređenih prstena i polja. Definirao se pojam niza te opisala konvergencija nizova u uređenim prstenima. U drugom se poglavlju proučavalo Cauchyjeve nizove u uređenim poljima. Uveden je pojam relacije ekvivalencije na skupu svih Cauchyjevih nizova u uređenom polju te pripadni kvocijentni skup. Definirane su binarne operacije \(\oplus \) i \(\odot\) na skupu \(\mathcal{C}(P,+,\cdot, \leqslant)/_{\thicksim}\) te dokazano da je \( (\mathcal{C}(P,+,\cdot, \leqslant)/_{\thicksim}, \oplus, \odot) \) polje. Na kraju je definirana relacija uređaja \(\preceq\) na \(\mathcal{C}(P,+,\cdot, \leqslant)/_{\thicksim}\) te je dokazano da je \( (\mathcal{C}(P,+,\cdot, \leqslant)/_{\thicksim}, \oplus, \odot, \preceq) \) uređeno polje.
Abstract (english)
In this thesis through first chapter we studied ordered groups, ordered rings and fields. The concept of sequence was defined and we described convergence of sequence in ordered fields. In second chapter we studied Cauchy sequences in ordered fields. We introduced an equivalence relation on the set of all Cauchy sequences in an ordered field and a corresponding quotient set. We defined binary operations \(\oplus \) and \(\odot\) on the set \(\mathcal{C}(P,+,\cdot, \leqslant)/_{\thicksim}\) and proved that (\( (\mathcal{C}(P,+,\cdot, \leqslant)/_{\thicksim}, \oplus, \odot) \) is a field. Finally, we defined an order \(\preceq\) na \(\mathcal{C}(P,+,\cdot, \leqslant)/_{\thicksim}\) and we proved that je \( (\mathcal{C}(P,+,\cdot, \leqslant)/_{\thicksim}, \oplus, \odot, \preceq) \)is an ordered field.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:082688
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 on2021-03-25 12:28:29