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OverviewFrom 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 Factorizations: Algebraic, Combinatorial, and Analytic Theory offers a look at the present state of the theory in a single, unified resource. Taking a broad look at the algebraic, combinatorial, and analytic fundamentals, this book derives factorization results and applies them in concrete arithmetical situations using appropriate transfer principles. It begins with a basic introduction that can be understood with knowledge of standard basic algebra. The authors then move to the algebraic theory of monoids, arithmetic theory of monoids, the structure of sets of lengths, additive group theory, arithmetical invariants, and the arithmetic of Krull monoids. They also provide a self-contained introduction to abstract analytic number theory as well as a modern treatment of W. Narkiewicz's analytic theory of non-unique factorizations. Non-Unique Factorizations: Algebraic, Combinatorial, and Analytic Theory builds the discussion from first principles to applied problem solving, making it ideally suited to those not familiar with the theory as well as those who wish to deepen their understanding. Full Product DetailsAuthor: Alfred Geroldinger , Franz Halter-Koch , Franz Halter-Koch (University of Graz, Austria) , Earl TaftPublisher: Taylor & Francis Inc Imprint: Chapman & Hall/CRC Volume: 278 Dimensions: Width: 17.80cm , Height: 4.60cm , Length: 25.40cm Weight: 1.451kg ISBN: 9781584885764ISBN 10: 1584885769 Pages: 728 Publication Date: 13 January 2006 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsConcepts in Factorization Theory and Examples. Algebraic Theory of Monoids. Arithmetic Theory of Monoids. The structure of Sets of Lengths. Additive Group Theory. Arithmetical Invariants of Krull Monoids. Global Arithmetic of Krull Monoids. Abstract Analytic Number Theory. Analytic Theory of Non-Unique Factorizations. Appendix A: Abelian Groups. Appendix B: Complex Analysis. Appendix C: Theory of Integration. Appendix D: Polyhedral Cones. Bibliography. List of Symbols. Subject Index.ReviewsCombining methods of various branches of mathematics, it brings together a theory from classical results to topics reflecting the recent ideas. It is a nice book written in a precise, readable style. - In EMS Newsletter, September 2007 ""Combining methods of various branches of mathematics, it brings together a theory from classical results to topics reflecting the recent ideas. It is a nice book written in a precise, readable style."" – In EMS Newsletter, September 2007 """Combining methods of various branches of mathematics, it brings together a theory from classical results to topics reflecting the recent ideas. It is a nice book written in a precise, readable style."" – In EMS Newsletter, September 2007" Author InformationAlfred Geroldinger, Franz Halter-Koch Tab Content 6Author Website:Countries AvailableAll regions |
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