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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Rezola, Nolberto"],"institution":null,"degree_name":"Master of Arts in Mathematics","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Griffing, Gary"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-06-01T07:00:00Z","date_published":"2015-06-01T07:00:00Z","updated_at":"2026-07-24T01:52:53Z","subjects":["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"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.lib.csusb.edu/etd/205","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Griffing, Gary"]},{"key":"dc:creator","label":"Author","values":["Rezola, Nolberto"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2015-05-22T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Arts in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["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"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.lib.csusb.edu/etd/205"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Unique Prime Factorization of Ideals in the Ring of Algebraic Integers of an Imaginary Quadratic Number Field"]}]}],"canonical_facts":{"dc:contributor":["Griffing, Gary"],"dc:creator":["Rezola, Nolberto"],"dc:date.available":["2015-05-22T07:00:00Z"],"dc:description.abstract":["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.
"],"dc:identifier":["https://scholarworks.lib.csusb.edu/etd/205"],"dc:subject":["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"],"dc:title":["Unique Prime Factorization of Ideals in the Ring of Algebraic Integers of an Imaginary Quadratic Number Field"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Arts in Mathematics"]},"updated_at":"2026-07-24T01:52:53Z"}