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The Characterization of Finite Elasticities
Af: David J. Grynkiewicz Engelsk Paperback
SPAR
kr 134
The Characterization of Finite Elasticities
Af: David J. Grynkiewicz Engelsk Paperback
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.

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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.

Produktdetaljer
Sprog: Engelsk
Sider: 282
ISBN-13: 9783031148682
Indbinding: Paperback
Udgave:
ISBN-10: 3031148681
Udg. Dato: 27 okt 2022
Længde: 0mm
Bredde: 235mm
Højde: 155mm
Oplagsdato: 27 okt 2022
Forfatter(e): David J. Grynkiewicz
Forfatter(e) David J. Grynkiewicz


Kategori Algebraisk geometri


Sprog Engelsk


Indbinding Paperback


Sider 282


Udgave


Længde 0mm


Bredde 235mm


Højde 155mm

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