The Characterization of Finite Elasticities: Factorization Theory in Krull Monoids via Convex Geometry...

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David J. Grynkiewicz

The Characterization of Finite Elasticities

Factorization Theory in Krull Monoids via Convex Geometry

David J. Grynkiewicz

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English

Springer International Publishing AG
27 October 2022

Discrete mathematics; Algebra; Groups & group theory; Number theory; Geometry

Series: Lecture Notes in Mathematics

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.

By: David J. Grynkiewicz
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 1st ed. 2022
Volume: 2316
Dimensions: Height: 235mm, Width: 155mm,
Weight: 456g
ISBN: 9783031148682
ISBN 10: 3031148681
Series: Lecture Notes in Mathematics
Pages: 282
Publication Date: 27 October 2022
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Reviews for The Characterization of Finite Elasticities: Factorization Theory in Krull Monoids via Convex Geometry

“This work is a well-written and well-organized research monograph which is accessible for the non-specialist. It is a masterpiece of research in factorization theory and convex geometry.” (Alfred Geroldinger, Mathematical Reviews, July, 2024)