Realna kvadratna proširenja

master's thesis

• Title (english): Real square extensions
• Author: Lovro Sindičić
• Mentor: Boris Širola (mentor)
• Committee member: Boris Širola (predsjednik povjerenstva)
• Committee member: Mladen Vuković (član povjerenstva)
• Committee member: Andrej Dujella (član povjerenstva)
• Committee member: Marko Tadić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-12-01, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES

Abstract

U ovom radu govorimo o kvadratnim proširenjima polja racionalnih brojeva, i to prvenstveno realnim kvadratnim proširenjima. Polazeći od definicije i elementarnih pojmova algebre, pokazujemo karakteristike i konstrukcije općenitih kvadratnih proširenja. Nadalje definiramo ključne pojmove algebarski broj i algebarskog cijelog broja i navodimo bitne rezultate vezane za njih. Na kraju navodimo neke strukturne rezultate za prsten cijelih brojeva kao što su jedinice, ideali, prosti ideali i faktorizacija.

Abstract (english)

In this thesis we consider quadratic field extensions of the field of rational numbers, and in particular real quadratic extensions. We begin by definitions and basic concepts of algebra, and then we characterize quadratic field extensions in general case. Furthermore we introduce the key notions of an algebraic number and algebraic integer, and for them we present some relevant results. Finally we prove certain structural results for the rings of integers of real quadratic extensions; e.g, some concerning units, ideals, prime ideals and factorization.

• Keywords: kvadratna proširenja polja racionalnih brojeva; algebarski broj; prsten cijelih brojeva; ideali; prosti ideali; faktorizacija
• Keywords (english): quadratic field extensions of the field of rational numbers; algebraic number; rings of integers of real quadratic extensions; ideals; prime ideals; factorization
• Language: croatian
• URN:NBN: urn:nbn:hr:217:727230
• Study programme: Title: Mathematics and Computer Science Education; specializations in: Mathematics and Computer Science Education; Course: Mathematics and Computer Science Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2021-02-24 13:25:51