Combinatorial Factorization Theory by Alfred Geroldinger
This monograph invites readers into the study of factorization theory of Krull monoids and domains. A first of its kind, the book bridges the algebraic background and the specialized machinery of additive combinatorics needed for researchers interested in factorization theory. Beginning with the necessary tools from algebra, the opening chapter focuses on the arithmetic of monoids and its link with additive combinatorics. From here, chapters discuss the methods and results from relevant areas of additive combinatorics, with a special focus on zero-sum problems. In the latter chapters, these tools are used to study factorization in monoids of zero-sum sequences over finite abelian groups. In particular, length sets and the study of elasticities, along with the characterization problem for systems of length sets, are a highlight of the volume. All of these results then apply to factorization in any Krull monoid or Krull domain. With its careful curation of the last 20 years of research, Combinatorial Factorization Theory serves as a guiding research monograph for this growing area. The introductory materials make this book an appropriate entry point for experienced and prospective researchers interested in learning more about these fields. A grounding in graduate algebra is assumed, but no specialist knowledge is required.-
Quantum Field Theory
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Chevalley-Warning, Beyond and Beneath
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Non-Abelian Monopoles and Four-Manifold Topology
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Quantum Topology Via Modified Traces
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Abelian Varieties
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Discrete Convex Analysis
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The Cremona Group and Its Subgroups
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Fokker-Planck-Kolmogorov Equations
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Grid Homology for Knots and Links
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The Classification of the Finite Simple Groups, Number 6
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The Classification of the Finite Simple Groups, Number 7
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Braid and Knot Theory in Dimension Four
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Residuated Structures in Algebra and Logic
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Attractors for Degenerate Parabolic Type Equations
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Advanced Analytic Number Theory: L-functions
- Geometric Function Theory in the Unit Ball of $\mathbb{C}^n$
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Cohen-Macaulay Representations
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The Convenient Setting of Global Analysis
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Noncommutative Multivariable Operator Theory
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Singular Time-Homogeneous Ito Equations and PDEs
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Locally Solid Riesz Spaces with Applications to Economics
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Control and Nonlinearity
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Mixed Motives
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Ergodic Theory Via Joinings
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Ricci Solitons in Dimensions $4$ and Higher
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Vertex Algebras and Algebraic Curves
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Surgery on Compact Manifolds
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Univalent Functions in Quantum Probability Theory
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Perfectoid Spaces
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The Ricci Flow: Techniques and Applications
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Parabolic Geometries I
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Trees of Hyperbolic Spaces
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Foundations of Arithmetic Differential Geometry
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Algebraic Geometry for Scientists and Engineers
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Operators, Functions, and Systems
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Mirror Symmetry and Algebraic Geometry
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Geometric Analysis on Symmetric Spaces
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Self-Similar Groups
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Knotted Surfaces and Their Diagrams
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Alice and Bob Meet Banach
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Weak Convergence of Measures
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Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups
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Iwasawa Theory and Its Perspective, Volume 1
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Discrete-Time Dynamics of Structured Populations and Homogeneous Order-Preserving Operators
Alfred Geroldinger, University of Graz, Austria, David J. Grynkiewicz, University of Memphis, TN, and Qinghai Zhong, University of Graz, Austria
| SKU | Unavailable |
| ISBN 13 | 9781470484682 |
| ISBN 10 | 1470484684 |
| Title | Combinatorial Factorization Theory |
| Author | Alfred Geroldinger |
| Series | Mathematical Surveys And Monographs |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | American Mathematical Society |
| Year published | 2026-11-29 |
| Number of pages | 800 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |