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master's thesis
Prsteni cijelih brojeva kvadratnih polja
Zagreb: University of Zagreb, Faculty of Science, 2024. urn:nbn:hr:217:356771
Kurilovčan, Lucia
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Kurilovčan, L. (2024). Prsteni cijelih brojeva kvadratnih polja (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:356771

Kurilovčan, Lucia. "Prsteni cijelih brojeva kvadratnih polja." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:356771

Kurilovčan, Lucia. "Prsteni cijelih brojeva kvadratnih polja." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:356771

Kurilovčan, L. (2024). 'Prsteni cijelih brojeva kvadratnih polja', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:356771

Kurilovčan L. Prsteni cijelih brojeva kvadratnih polja [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2024 [cited 2024 November 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:356771

L. Kurilovčan, "Prsteni cijelih brojeva kvadratnih polja", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:217:356771

Metadata
TitlePrsteni cijelih brojeva kvadratnih polja
Title (english)Rings of integers of quadratic fields
AuthorLucia Kurilovčan
MentorZrinka Franušić (mentor)
MentorNikola Adžaga (sumentor)
Committee memberZrinka Franušić (predsjednik povjerenstva)
Committee memberTihomir Vukelja (član povjerenstva)
Committee memberNikola Adžaga (član povjerenstva)
Committee memberBojan Basrak (član povjerenstva)
Committee memberTomislav Bokulić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2024-05-02, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Neka je \(m\) cijeli broj koji nije potpuni kvadrat. Skup oblika \(\mathbb{Q}(\sqrt{m}) = \{ a+b \sqrt{m} : a,b \in \mathbb{Q} \}\), uz standardne operacije zbrajanja i množenja u \(\mathbb{C}\), čini polje i naziva se kvadratno polje. U radu se bavimo prstenima cijelih brojeva kvadratnih polja, to jest skupovima oblika \(\mathbb{Z}[\sqrt m]=\{a+b\sqrt{m}\ :\ a,b\in\mathbb{Z}\}\), za \(m \equiv 2\) ili \(3\pmod{4}\) i \(\mathbb{Z}\left[\frac{1+\sqrt m}{2}\right]=\left\{ \frac{a+b\sqrt{m}}{2} \ : \ a,b \in \mathbb{Z}, \ a \equiv b \pmod{2} \right\},\) za \(m \equiv 1\pmod{4}\), te problemom faktorizacije na ireducibilne faktore u tim prstenima.
Abstract (english)
Let \(m\) be an integer that is not a perfect square. A set of the form \(\mathbb{Q}(\sqrt{m}) = \{ a+b \sqrt{m} : a,b \in \mathbb{Q} \}\), with standard addition and multiplication in \(\mathbb{C}\), forms a field and is called a quadratic field. In the thesis, we deal with rings of integers of quadratic fields, that is, sets of the form \(\mathbb{Z}[\sqrt m]=\{a+b\sqrt{m}\ :\ a,b\in\mathbb{Z}\}\), for \(m \equiv 2\) or \(3\pmod{4}\) and \(\mathbb{Z}\left[\frac{1+\sqrt m}{2}\right]=\left\{ \frac{a+b\sqrt{m}}{2} \ : \ a,b \in \mathbb{Z}, \ a \equiv b \pmod{2} \right\},\) for \(m \equiv 1\pmod{4}\), and with the factorization problem in these rings.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:356771
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: sveučilišni magistar edukacije matematike i fizike (sveučilišni magistar edukacije matematike i fizike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-05-22 09:27:03