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The Characterization of Finite Elasticities : Factorization Theory in Krull Monoids via Convex Geometry / by David J. Grynkiewicz.
- Format:
- Book
- Author/Creator:
- Grynkiewicz, David J., Author.
- Series:
- Mathematics and Statistics (SpringerNature-11649)
- Lecture Notes in Mathematics, 1617-9692 ; 2316
- Language:
- English
- Subjects (All):
- Number theory.
- Commutative algebra.
- Commutative rings.
- Group theory.
- Convex geometry.
- Discrete geometry.
- Number Theory.
- Commutative Rings and Algebras.
- Group Theory and Generalizations.
- Convex and Discrete Geometry.
- Local Subjects:
- Number Theory.
- Commutative Rings and Algebras.
- Group Theory and Generalizations.
- Convex and Discrete Geometry.
- Physical Description:
- 1 online resource (XII, 282 pages) : 1 illustrations
- Edition:
- 1st edition 2022.
- Contained In:
- Springer Nature eBook
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2022.
- System Details:
- text file PDF
- Summary:
- This book develops a new theory in convex geometry, generalizing positive bases and related to Carathéordory's Theorem by combining convex geometry, the combinatorics of infinite subsets of lattice points, and the arithmetic of transfer Krull monoids (the latter broadly generalizing the ubiquitous class of Krull domains in commutative algebra) This new theory is developed in a self-contained way with the main motivation of its later applications regarding factorization. While factorization into irreducibles, called atoms, generally fails to be unique, there are various measures of how badly this can fail. Among the most important is the elasticity, which measures the ratio between the maximum and minimum number of atoms in any factorization. Having finite elasticity is a key indicator that factorization, while not unique, is not completely wild. Via the developed material in convex geometry, we characterize when finite elasticity holds for any Krull domain with finitely generated class group $G$, with the results extending more generally to transfer Krull monoids. This book is aimed at researchers in the field but is written to also be accessible for graduate students and general mathematicians.
- Other Format:
- Printed edition:
- ISBN:
- 978-3-031-14869-9
- 9783031148699
- Access Restriction:
- Restricted for use by site license.
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