Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 106
Book Description
Some Types of Unique Factorization in Integral Domains
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 106
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 106
Book Description
Factorization in Integral Domains
Author: Daniel Anderson
Publisher: Routledge
ISBN: 1351448935
Category : Mathematics
Languages : en
Pages : 452
Book Description
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.
Publisher: Routledge
ISBN: 1351448935
Category : Mathematics
Languages : en
Pages : 452
Book Description
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.
A Study of Unique Factorization in Quadratic Integral Domains
Author: Ronald Lee Van Enkevort
Publisher:
ISBN:
Category : Algebraic fields
Languages : en
Pages : 110
Book Description
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.
Publisher:
ISBN:
Category : Algebraic fields
Languages : en
Pages : 110
Book Description
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.
Factoring Ideals in Integral Domains
Author: Marco Fontana
Publisher: Springer Science & Business Media
ISBN: 3642317111
Category : Mathematics
Languages : en
Pages : 170
Book Description
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.
Publisher: Springer Science & Business Media
ISBN: 3642317111
Category : Mathematics
Languages : en
Pages : 170
Book Description
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.
Restoring Factorization in Integral Domains
Author: Susan L. Kirk
Publisher:
ISBN:
Category :
Languages : en
Pages : 70
Book Description
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.
Publisher:
ISBN:
Category :
Languages : en
Pages : 70
Book Description
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.
Integral Domains Inside Noetherian Power Series Rings: Constructions and Examples
Author: William Heinzer
Publisher: American Mathematical Soc.
ISBN: 1470466422
Category : Education
Languages : en
Pages : 426
Book Description
Power series provide a technique for constructing examples of commutative rings. In this book, the authors describe this technique and use it to analyse properties of commutative rings and their spectra. This book presents results obtained using this approach. The authors put these results in perspective; often the proofs of properties of classical examples are simplified. The book will serve as a helpful resource for researchers working in commutative algebra.
Publisher: American Mathematical Soc.
ISBN: 1470466422
Category : Education
Languages : en
Pages : 426
Book Description
Power series provide a technique for constructing examples of commutative rings. In this book, the authors describe this technique and use it to analyse properties of commutative rings and their spectra. This book presents results obtained using this approach. The authors put these results in perspective; often the proofs of properties of classical examples are simplified. The book will serve as a helpful resource for researchers working in commutative algebra.
Factorization in Integral Domains
Author: Samuel Borofsky
Publisher:
ISBN:
Category :
Languages : en
Pages : 46
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 46
Book Description
Factorization
Author: Steven H. Weintraub
Publisher: CRC Press
ISBN: 1439865663
Category : Mathematics
Languages : en
Pages : 270
Book Description
The concept of factorization, familiar in the ordinary system of whole numbers that can be written as a unique product of prime numbers, plays a central role in modern mathematics and its applications. This exposition of the classic theory leads the reader to an understanding of the current knowledge of the subject and its connections to other math
Publisher: CRC Press
ISBN: 1439865663
Category : Mathematics
Languages : en
Pages : 270
Book Description
The concept of factorization, familiar in the ordinary system of whole numbers that can be written as a unique product of prime numbers, plays a central role in modern mathematics and its applications. This exposition of the classic theory leads the reader to an understanding of the current knowledge of the subject and its connections to other math
Integral Closure of Ideals, Rings, and Modules
Author: Craig Huneke
Publisher: Cambridge University Press
ISBN: 0521688604
Category : Mathematics
Languages : en
Pages : 446
Book Description
Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Publisher: Cambridge University Press
ISBN: 0521688604
Category : Mathematics
Languages : en
Pages : 446
Book Description
Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Non-Unique Factorizations
Author: Alfred Geroldinger
Publisher: CRC Press
ISBN: 1420003208
Category : Mathematics
Languages : en
Pages : 723
Book Description
From its origins in algebraic number theory, the theory of non-unique factorizations has emerged as an independent branch of algebra and number theory. Focused efforts over the past few decades have wrought a great number and variety of results. However, these remain dispersed throughout the vast literature. For the first time, Non-Unique Factoriza
Publisher: CRC Press
ISBN: 1420003208
Category : Mathematics
Languages : en
Pages : 723
Book Description
From its origins in algebraic number theory, the theory of non-unique factorizations has emerged as an independent branch of algebra and number theory. Focused efforts over the past few decades have wrought a great number and variety of results. However, these remain dispersed throughout the vast literature. For the first time, Non-Unique Factoriza