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Zusatztext "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 Informationen zum Autor Alfred Geroldinger, Franz Halter-Koch Klappentext This monograph-the first of its kind-presents the current state of knowledge on the theory of non-unique factorizations along with a broad discussion of its algebraic! combinatorial! and analytic fundamentals. The book focuses on factorization properties in rings of integers! orders of algebraic number fields! holomorphy rings! Krull and Mori domains! Krull monoids! congruence monoids! Hilbert monoids! and zero-sum sequences over Abelian groups. It also includes self-contained introductions to the v-ideal theory of monoids! additive group theory! and abstract analytic number theory. Within this treatment! the authors unify! extend! and put into a new context many known algebraic! combinatorial! and analytic results. Zusammenfassung 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. Inhaltsverzeichnis CONCEPTS IN FACTORIZATION THEORY AND EXAMPLESAtoms and PrimesFree Monoids! Factorial Monoids and FactorizationsBF-MonoidsSystems of Sets of LengthsFF-MonoidsThe Catenary Degree and the Tame DegreeRings of Integers of Algebraic Number FieldsALGEBRAIC THEORY OF MONOIDSv-IdealsPrime Ideals and LocalizationsComplete Integral Closures and Krull MonoidsDivisor Homomorphisms and Divisor TheoriesKrull Monoids and Class GroupsDefining Systems and v-Noetherian MonoidsFinitary MonoidsClass SemigroupsC-Monoids and Finitely Primary MonoidsIntegral DomainsCongruence Monoids and OrdersARITHMETIC THEORY OF MONOIDSFinitary MonoidsTransfer PrinciplesC-MonoidsSaturated Submonoids and Krull MonoidsType MonoidsFaithfully Saturated SubmonoidsIntegral Domains and Congruence MonoidsFactorizations of Powers of an ElementTHE STRUCTURE OF SETS OF LENGTHSMultidimensional Arithmetical ProgressionsAlmost Arithmetical MultiprogressionsAn Abstract Structure Theorem for Sets of LengthsPattern Ideals and Complete s-Ideals in Finitary MonoidsProducts of Strongly Primary Monoids and their SubmonoidsC-MonoidsIntegral Domains and Congruence MonoidsRealization Theorems and Further ExamplesSets of Lengths of Powers of an ElementADDITIVE GROUP THEORYSequences over Abelian GroupsAddition TheoremsZero-Sumfree SequencesCyclic GroupsGroup Algebras and p-GroupsCoverings by Cosets and Elementary p-GroupsShort Zero-Sum Sequences and the Inductive MethodGroups of Rank TwoARITHMETICAL INVARIANTS OF KRULL MONOIDSThe Generalized Davenport ConstantsThe Narkiewicz ConstantsThe Elasticity and Its RefinementsThe Catenary DegreeThe Tame DegreeSets of Lengths Containing 2The Set of Distances and Maximal Half-Factorial SetsMinimal Non-Half-Factorial SetsGLOBAL ARITHMETIC OF KRULL MONOIDSArithmetical Characterizations of Class Groups IArithmetical Characterizations of Class Groups IIThe System of Sets of Lengths for Finite Abelian GroupsThe System of Sets of Lengths for Infinite Abelian GroupsAdditively Closed Sequences and Restricted SumsetsFactorization of Large ElementsABSTRACT ANALYTIC NUMBER THEORYDirichlet SeriesA General Tauberian TheoremAbstract Formations and Zeta FunctionsArithmetical Formations I: Zeta FunctionsArithmetical Formations II: Asymptotic ResultsArithmetical Formations III: Structure TheoryGeometrical Formations I: Asymptotic ResultsGeometrical Formations II: Structure TheoryAlgebraic Function FieldsObstructed FormationsANALYTIC THEORY OF NON-UNIQUE FACTORIZATIONSAnalytic Theory of TypesElements with ...
