Download or read book Restoring Factorization in Integral Domains written by Susan L. Kirk and published by . This book was released on 2015 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Factorization in Integral Domains written by Daniel Anderson and published by Routledge. This book was released on 2017-11-13 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Factorization in Integral Domains written by Daniel Anderson and published by CRC Press. This book was released on 1997-04-22 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Study of Unique Factorization in Quadratic Integral Domains written by Ronald Lee Van Enkevort and published by . This book was released on 1967 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Factoring Ideals in Integral Domains written by Marco Fontana and published by Springer Science & Business Media. This book was released on 2013 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Factorization in Integral Domains written by Samuel Borofsky and published by . This book was released on 1939 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Factorization in Integral Domains Without Identity written by Jonathan Preisser and published by . This book was released on 2009 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Factorization in Integral Domains written by Klara J. Cohn and published by . This book was released on 1994 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quadratic Integral Domains in Ra square Root 5 and Ra square Root 13 written by Adelbert Frederick Hackert and published by . This book was released on 1966 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some of the properties of the numbers of two quadratic number fields are explored. Among these properties is the existence of unique prime factorization of the integers of the field and the importance of the concept of ideal numbers in restoring unique factorization when it does not exist. Some consideration is given to the relationship between the nature of the ideals of an integral domain and the existence of unique factorization in that domain.
Download or read book Some Types of Unique Factorization in Integral Domains written by and published by . This book was released on 1968 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Factorization in Integral Domains written by Samuel Borofsky and published by . This book was released on 1939 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Quadratic Integral Domains Ra square Root 3 and Ra square Root 15 written by Sue Elaine Hardy Waldman and published by . This book was released on 1967 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is the record of an exploration of two quadratic number fields. The first section is devoted to the field with elements of the form a +b√3 where a and b are rational numbers. This field contains an integral domain in which unique factorization holds. The second section is concerned with a field having an integral domain in which the unique factorization theorem does not hold; therefore ideals are introduced to restore this property. The elements of this field are of the form a +b √-l5 where a and b are rational numbers.
Download or read book Integral Domains Not Possessing the Unique Factorization Property written by Mary Buterbaugh Kline and published by . This book was released on 1971 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Generalized Factorization in Integral Domains written by Andrea Marie Frazier and published by . This book was released on 2006 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Results on Factorization in Integral Domains written by Jack Robert Bennett and published by . This book was released on 2011 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we study three recent generalizations of unique factorization; the almost Schreier property, the inside factorial property, and the IDPF property. Let R be an integral domain and let p be a nonzero element of R. Then, p is said to be almost primal if whenever p [vertical line] xy, there exists an integer k [greater than or equal to] 1 and p 1, p 2 [is an element of] R such that p k = p 1 p 2 with p 1 [vertical line] x k and p 2 [vertical line] y k . R is said to be almost Schreier if every nonzero element of R is almost primal. Given an M -graded domain R = [tensor product of modules] m [is an element of] M R m, where M is a torsion-free, commutative, cancellative monoid, we classify when R is almost Schreier under the assumption that R [is a subset of] R is a root extension. We then specialize to the case of commutative semigroup rings and show that if R [M] [is a subset of] [Special characters omitted.] is a root extension, then R [M] is almost Schreier if and only if R is an almost Schreier domain and M is an almost Schreier monoid.
Download or read book A Study of Factorization in the Integral Domains Ra square Root 2 and Ra square Root 31 written by Nancy Darlene Plotner and published by . This book was released on 1968 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Description of Three Integral Domains Considering Divisibility and Factorization written by Robert L. Smith and published by . This book was released on 1966 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt:
