Non-Unique Factorizations: Algebraic, Combinatorial and Analytic Theory

Alfred Geroldinger, Franz Halter-Koch

January 13, 2006 by Chapman and Hall/CRC
Reference - 728 Pages - 7 B/W Illustrations
ISBN 9781584885764 - CAT# C5769
Series: Chapman & Hall/CRC Pure and Applied Mathematics

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  • Provides a thorough presentation of the current state of knowledge in the theory of non-unique factorizations
  • Focuses on the algebraic, combinatorial, and analytical aspects of the theory
  • Offers self-contained sections on the fundamentals of v-ideal theory, additive group theory, and analytic number theory
  • Presents a discussion on additive group theory, paying special attention to recent developments and focusing on finite Abelian groups
  • Focuses on the Prime Element Theorem for formations with remainder terms and on Tauberian Theorems for arithmetically defined Dirichlet series
  • Summary

    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 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.