Non-Unique Factorizations : Algebraic, Combinatorial and Analytic Theory
Non-Unique Factorizations : Algebraic, Combinatorial and Analytic Theory
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DOI：
10.1201/9781420003208
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发表时间：
2006-01
期刊：
影响因子：
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通讯作者：
A. Geroldinger;F. Halter-Koch
中科院分区：
文献类型：
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作者：
A. Geroldinger;F. Halter-Koch
因式分解理论中的概念和例子原子和素自由幺半群，阶乘幺半群和因子分解BF-幺半群系统的集的LQFF-幺半群的悬链线度和驯服度环的整数代数数域代数理论的幺半群v-理想素理想和局部化完整的积分闭包和Krull幺半群因子同态和因子理论Krull幺半群和类群定义系统和v-Noether幺半群有限幺半群类半群C-幺半群与非准素幺半群整域同余幺半群与阶幺半群有限幺半群转移原理C-幺半群饱和子幺半群与Krull型幺半群忠实饱和子幺半群整域与同余幺半群元幂的分解长集的结构多维等差数列几乎算术多重级数有限幺半群中L型理想和完全s-理想集的抽象结构定理强准素幺半群及其子幺半群的乘积C-幺半群整域和同余幺半群的实现定理及进一步的例子元素幂的L型集阿贝尔群上的加法群论序列加法定理零和自由序列循环群代数和p-群的陪集覆盖与初等p-群的短零和序列与归纳法秩二的Krnish么半群的ARMMETCAL不变量群广义Davenport常数Narkiewicz常数弹性及其加细悬链线度含2的Lés的驯服度集距离集与极大半阶乘集极小非半阶乘集阶乘集Krichlet幺半群的整体代数群的算术特征Ⅰ群的算术特征Ⅱ有限阿贝尔群的线性集系无限阿贝尔群的线性集系加性闭序列与限制和集大元素的因式分解抽象解析数论Dirichlet级数A一般Tauberian定理抽象形式和Zeta函数算术形式I：Zeta函数算术形式II：渐近结果算术形式III：结构理论几何形式I：渐近结果几何形式II：结构理论代数函数场阻塞形成非线性分析理论唯一因式分解类型分析理论具有规定因式分解性质的元素不同因式分解的数目块相关因式分解性质附录A：阿贝尔群附录B：复合物分析附录C：积分理论附录D：多面体圆锥体参考书目符号表
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