Unique Prime Factorization of Ideals in the Ring of Algebraic Integers of an Imaginary Quadratic Number Field

<p>The ring of integers is a very interesting ring, it has the amazing property that each of its elements may be expressed uniquely, up to order, as a product of prime elements. Unfortunately, not every ring possesses this property for its elements. The work of mathematicians like Kummer and Dedekind lead to the study of a special type of ring, which we now call a Dedekind domain, where even though unique prime factorization of elements may fail, the ideals of a Dedekind domain still enjoy the property of unique prime factorization into a product of prime ideals, up to order of the factors. This thesis seeks to establish the unique prime ideal factorization of ideals in a special type of Dedekind domain: the ring of algebraic integers of an imaginary quadratic number field.</p>

Name thesis:degree_name

Master of Arts in Mathematics

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2015

Author dc:creator

• Rezola, Nolberto

Contributors dc:contributor

• Griffing, Gary

• imaginary quadratic number field
• unique prime ideal factorization
• Dedekind domain
• Algebraic integers
• Rings
• Fields
• Ideals
• Integral over
• R-modules
• finitely generated set
• UFD
• PID.
• Algebra
• Number Theory
• Other Mathematics

Repository record dc:identifier

https://scholarworks.lib.csusb.edu/etd/205

OAI identifier oai:identifier

oai:scholarworks.lib.csusb.edu:etd-1223