Non-Unique Factorizations - Alfred Geroldinger, Franz Halter-Koch

Non-Unique Factorizations

Algebraic, Combinatorial and Analytic Theory
Buch | Hardcover
728 Seiten
2006
Chapman & Hall/CRC (Verlag)
978-1-58488-576-4 (ISBN)
229,95 inkl. MwSt
Presents the knowledge on the theory of non-unique factorizations and discusses its algebraic, combinatorial, and analytic fundamentals. This book focuses on factorization properties in rings of integers, orders of algebraic number fields, holomorphy rings, Krull and Mori domains, Krull monoids, congruence monoids, and Hilbert monoids.
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.

Alfred Geroldinger, Franz Halter-Koch

Concepts 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.

Erscheint lt. Verlag 13.1.2006
Reihe/Serie Chapman & Hall/CRC Pure and Applied Mathematics
Zusatzinfo 7 Illustrations, black and white
Sprache englisch
Maße 178 x 254 mm
Gewicht 1451 g
Themenwelt Mathematik / Informatik Mathematik Arithmetik / Zahlentheorie
ISBN-10 1-58488-576-9 / 1584885769
ISBN-13 978-1-58488-576-4 / 9781584885764
Zustand Neuware
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