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Some Results On Factorization In Integral Domains
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Book Synopsis Factorization in Integral Domains by : Daniel Anderson
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.
Book Synopsis Factorization in Integral Domains by : Daniel Anderson
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.
Book Synopsis Some Results on Factorization in Integral Domains by : Jack Robert Bennett
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.
Book Synopsis Factorization in Integral Domains by : Daniel Anderson
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 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.
Book Synopsis Factoring Ideals in Integral Domains by : Marco Fontana
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.
Book Synopsis Factorization in Integral Domains by : Samuel Borofsky
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:
Book Synopsis Some Types of Unique Factorization in Integral Domains by :
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:
Book Synopsis Factorization by : Steven H. Weintraub
Download or read book Factorization written by Steven H. Weintraub and published by CRC Press. This book was released on 2008-05-15 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Factorization in Integral Domains by : Samuel Borofsky
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:
Book Synopsis From Polynomials to Sums of Squares by : T.H Jackson
Download or read book From Polynomials to Sums of Squares written by T.H Jackson and published by CRC Press. This book was released on 2023-05-09 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Polynomials to Sums of Squares describes a journey through the foothills of algebra and number theory based around the central theme of factorization. The book begins by providing basic knowledge of rational polynomials, then gradually introduces other integral domains, and eventually arrives at sums of squares of integers. The text is complemented with illustrations that feature specific examples. Other than familiarity with complex numbers and some elementary number theory, very little mathematical prerequisites are needed. The accompanying disk enables readers to explore the subject further by removing the tedium of doing calculations by hand. Throughout the text there are practical activities involving the computer.
Book Synopsis Integral Domains Inside Noetherian Power Series Rings: Constructions and Examples by : William Heinzer
Download or read book Integral Domains Inside Noetherian Power Series Rings: Constructions and Examples written by William Heinzer and published by American Mathematical Soc.. This book was released on 2021-10-08 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Arithmetical Properties of Commutative Rings and Monoids by : Scott T. Chapman
Download or read book Arithmetical Properties of Commutative Rings and Monoids written by Scott T. Chapman and published by CRC Press. This book was released on 2005-03-01 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of nonunique factorizations of elements into irreducible elements in commutative rings and monoids has emerged as an independent area of research only over the last 30 years and has enjoyed a recent flurry of activity and advancement. This book presents the proceedings of two recent meetings that gathered key researchers from around the w
Download or read book Basic Algebra written by Anthony W. Knapp and published by Springer Science & Business Media. This book was released on 2007-07-28 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems.
Book Synopsis Non-Unique Factorizations by : Alfred Geroldinger
Download or read book Non-Unique Factorizations written by Alfred Geroldinger and published by CRC Press. This book was released on 2006-01-13 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Trends in Commutative Rings Research by : Ayman Badawi
Download or read book Trends in Commutative Rings Research written by Ayman Badawi and published by Nova Publishers. This book was released on 2004 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Trends in Commutative Rings Research
Book Synopsis Abstract Algebra by : Jonathan K. Hodge
Download or read book Abstract Algebra written by Jonathan K. Hodge and published by CRC Press. This book was released on 2013-12-21 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizing active learning, this text not only teaches abstract algebra but also provides a deeper understanding of what mathematics is, how it is done, and how mathematicians think. The book can be used in both rings-first and groups-first abstract algebra courses. Numerous activities, examples, and exercises illustrate the definitions, theorems, and concepts. Each chapter also discusses the connections among topics in ring theory and group theory, helping students see the relationships between the two main types of algebraic objects studied throughout the text.
Book Synopsis Advances in Commutative Ring Theory by : David Dobbs
Download or read book Advances in Commutative Ring Theory written by David Dobbs and published by CRC Press. This book was released on 2023-08-25 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Presents the proceedings of the recently held Third International Conference on Commutative Ring Theory in Fez, Morocco. Details the latest developments in commutative algebra and related areas-featuring 26 original research articles and six survey articles on fundamental topics of current interest. Examines wide-ranging developments in commutative algebra, together with connections to algebraic number theory and algebraic geometry."
