Factorization in Integral Domains
Title | Factorization in Integral Domains PDF eBook |
Author | Daniel Anderson |
Publisher | Routledge |
Pages | 448 |
Release | 2017-11-13 |
Genre | Mathematics |
ISBN | 1351448943 |
The contents in this work are taken from both the University of Iowa's Conference on Factorization in Integral Domains, and the 909th Meeting of the American Mathematical Society's Special Session in Commutative Ring Theory held in Iowa City. The text gathers current work on factorization in integral domains and monoids, and the theory of divisibility, emphasizing possible different lengths of factorization into irreducible elements.
Restoring Factorization in Integral Domains
Title | Restoring Factorization in Integral Domains PDF eBook |
Author | Susan L. Kirk |
Publisher | |
Pages | 70 |
Release | 2015 |
Genre | |
ISBN |
This is an expository thesis on integral domains which are not unique factorization domains. We focus on restoring a type of unique factorization using prime ideals within quadratic integer rings. In particular, we examine which quadratic integer rings will admit such factorization.
Factorization in Integral Domains
Title | Factorization in Integral Domains PDF eBook |
Author | Daniel Anderson |
Publisher | CRC Press |
Pages | 452 |
Release | 1997-04-22 |
Genre | Mathematics |
ISBN | 9780824700324 |
The contents in this work are taken from both the University of Iowa's Conference on Factorization in Integral Domains, and the 909th Meeting of the American Mathematical Society's Special Session in Commutative Ring Theory held in Iowa City. The text gathers current work on factorization in integral domains and monoids, and the theory of divisibility, emphasizing possible different lengths of factorization into irreducible elements.
Factorization in Integral Domains
Title | Factorization in Integral Domains PDF eBook |
Author | Samuel Borofsky |
Publisher | |
Pages | 46 |
Release | 1939 |
Genre | |
ISBN |
Factoring Ideals in Integral Domains
Title | Factoring Ideals in Integral Domains PDF eBook |
Author | Marco Fontana |
Publisher | Springer Science & Business Media |
Pages | 170 |
Release | 2013 |
Genre | Mathematics |
ISBN | 3642317111 |
This volume provides a wide-ranging survey of, and many new results on, various important types of ideal factorization actively investigated by several authors in recent years. Examples of domains studied include (1) those with weak factorization, in which each nonzero, nondivisorial ideal can be factored as the product of its divisorial closure and a product of maximal ideals and (2) those with pseudo-Dedekind factorization, in which each nonzero, noninvertible ideal can be factored as the product of an invertible ideal with a product of pairwise comaximal prime ideals. Prüfer domains play a central role in our study, but many non-Prüfer examples are considered as well.
A Study of Unique Factorization in Quadratic Integral Domains
Title | A Study of Unique Factorization in Quadratic Integral Domains PDF eBook |
Author | Ronald Lee Van Enkevort |
Publisher | |
Pages | 110 |
Release | 1967 |
Genre | Algebraic fields |
ISBN |
This thesis studies the question of unique factorization in quadratic integral domains. In the first chapter many general theorems and definitions from algebraic number theory are introduced. The second chapter considers an integral domain in which unique factorization holds. The necessary theorems to prove unique factorization are developed. The third chapter concerns an integral domain in which unique factorization fails. That it fails is proved and then ideals are introduced to indicate how unique factorization would be restored in terms of ideals.
Factorization in Integral Domains Without Identity
Title | Factorization in Integral Domains Without Identity PDF eBook |
Author | Jonathan Preisser |
Publisher | |
Pages | 88 |
Release | 2009 |
Genre | Factorization (Mathematics) |
ISBN |