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On Integers, Primes and UniqueFactorization in Quadratic Fields
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2013 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]


This thesis will deal with quadratic elds. The prob-

lem is to study such elds and their properties including, but not

limited to, determining integers, nding primes and deciding which

quadratic elds have unique factorization. The goal is to get famil-

iar with these concepts and to provide a starting point for students

with an interest in algebra to explore eld extensions and inte-

gral closures in relation to elementary number theory. The reader

will be assumed to have a basic knowledge in algebra and famil-

iar with concepts such as groups, rings and elds. The necessary

background material is covered in for example

A First Course In

Abstract Algebra

by John B. Fraleigh. Some familiarity with basic

number theory may be helpful, but not necessary for the scope of

this thesis. The questions posed in this thesis was answered by

means of literature and discussions with fellow students and my


The rst four sections will deal with basic concepts in algebra such

as algebraic numbers, algebraic integers and prime numbers. This

knowledge will then be applied to the subject of quadratic elds.

The thesis is concluded with two sections about important cases

of quadratic elds, Gaussian and Eisenstein.

Place, publisher, year, edition, pages
2013. , 22 p.
National Category
Engineering and Technology
URN: urn:nbn:se:kth:diva-127662OAI: diva2:644820
Available from: 2013-09-02 Created: 2013-09-02 Last updated: 2013-09-02Bibliographically approved

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