Date of Award

1-1-2014

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (v, 64 pages) : illustrations.

Dissertation/Thesis Chair

Anupam Srivastav

Committee Members

Marco Varisco, Alexandre Tchernev

Keywords

algebraic number theory, class group, kernel group, number theory, Rings (Algebra), Ideals (Algebra), k-groups

Subject Categories

Physical Sciences and Mathematics

Abstract

Given a number field k with ring of algebraic integers o(k), define an equivalence relation by declaring that two ideals a and b lie in the same class if and only if there exist non-zero elements c and d such that ca = db. These classes form an abelian group called the ideal class group of o(k), abbreviated Cl(o(k)). This group, in some sense, measures how different a ring of algebraic integers is from a principal ideal domain.

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