Non-unique factorizations : algebraic, combinatorial and analytic theory

CONCEPTS IN FACTORIZATION THEORY AND EXAMPLES Atoms and Primes Free Monoids, Factorial Monoids and Factorizations BF-Monoids Systems of Sets of Lengths FF-Monoids The Catenary Degree and the Tame Degree Rings of Integers of Algebraic Number Fields ALGEBRAIC THEORY OF MONOIDS v-Ideals Prime Ideals and Localizations Complete Integral Closures and Krull Monoids Divisor Homomorphisms and Divisor Theories Krull Monoids and Class Groups Defining Systems and v-Noetherian Monoids Finitary Monoids Class Semigroups C-Monoids and Finitely Primary Monoids Integral Domains Congruence Monoids and Orders ARITHMETIC THEORY OF MONOIDS Finitary Monoids Transfer Principles C-Monoids Saturated Submonoids and Krull Monoids Type Monoids Faithfully Saturated Submonoids Integral Domains and Congruence Monoids Factorizations of Powers of an Element THE STRUCTURE OF SETS OF LENGTHS Multidimensional Arithmetical Progressions Almost Arithmetical Multiprogressions An Abstract Structure Theorem for Sets of Lengths Pattern Ideals and Complete s-Ideals in Finitary Monoids Products of Strongly Primary Monoids and their Submonoids C-Monoids Integral Domains and Congruence Monoids Realization Theorems and Further Examples Sets of Lengths of Powers of an Element ADDITIVE GROUP THEORY Sequences over Abelian Groups Addition Theorems Zero-Sumfree Sequences Cyclic Groups Group Algebras and p-Groups Coverings by Cosets and Elementary p-Groups Short Zero-Sum Sequences and the Inductive Method Groups of Rank Two ARITHMETICAL INVARIANTS OF KRULL MONOIDS The Generalized Davenport Constants The Narkiewicz Constants The Elasticity and Its Refinements The Catenary Degree The Tame Degree Sets of Lengths Containing 2 The Set of Distances and Maximal Half-Factorial Sets Minimal Non-Half-Factorial Sets GLOBAL ARITHMETIC OF KRULL MONOIDS Arithmetical Characterizations of Class Groups I Arithmetical Characterizations of Class Groups II The System of Sets of Lengths for Finite Abelian Groups The System of Sets of Lengths for Infinite Abelian Groups Additively Closed Sequences and Restricted Sumsets Factorization of Large Elements ABSTRACT ANALYTIC NUMBER THEORY Dirichlet Series A General Tauberian Theorem Abstract Formations and Zeta Functions Arithmetical Formations I: Zeta Functions Arithmetical Formations II: Asymptotic Results Arithmetical Formations III: Structure Theory Geometrical Formations I: Asymptotic Results Geometrical Formations II: Structure Theory Algebraic Function Fields Obstructed Formations ANALYTIC THEORY OF NON-UNIQUE FACTORIZATIONS Analytic Theory of Types Elements with Prescribed Factorization Properties The Number of Distinct Factorizations Block-Dependent Factorization Properties APPENDIX A: ABELIAN GROUPS APPENDIX B: COMPLEX ANALYSIS APPENDIX C: THEORY OF INTEGRATION APPENDIX D: POLYHEDRAL CONES BIBLIOGRAPHY LIST OF SYMBOLS SUBJECT INDEX