Integer-Valued Polynomials: From Combinatorics to Number Theory, $p$-adic Analysis, Commutative and Non-Commutative Algebra - Couverture rigide

Chabert, Jean-Luc

 
9781470482060: Integer-Valued Polynomials: From Combinatorics to Number Theory, $p$-adic Analysis, Commutative and Non-Commutative Algebra
Couverture rigide
ISBN 10 : 1470482061 ISBN 13 : 9781470482060
Editeur : American Mathematical Society, 2026

Synopsis

This book presents the theory of integer-valued polynomials, as transformed by the work of Manjul Bhargava in the late 1990s. Building from the core ideas in commutative algebra and number theory, the author weaves a panoramic perspective that encompasses results in combinatorics, ultrametric analysis, probability, dynamical systems, and non-commutative algebra. Whether already established in the area or just starting out, readers will find this deep and approachable treatment to be an essential companion to research. Grouped into seven parts, the book begins with the preliminaries of integer-valued polynomials on $\mathbb{Z }$ and subsets of $\mathbb{Z}$. Bhargava's revolutionary orderings and generalized factorials follow, laying the foundation for the modern perspective, before an interlude on algebraic number theory explores the Polya group. Connections between topology and multiplicative ideal theory return the focus to commutative algebra, providing tools for exploring Prufer domains. A part on ultrametric analysis ranges across $p$-adic extensions of the Stone-Weierstrass theorem, new orderings, and dynamics. Chapters on asymptotic densities and polynomials in several variables precede the final part on non-commutative algebra. Exercises and historical remarks engage the reader throughout. A thoroughly modern sequel to the author's 1997 Integer-Valued Polynomials with Paul-Jean Cahen, this book welcomes readers with a grounding in commutative algebra and number theory at the level of Dedekind domains. No specialist knowledge of probability, dynamics, or non-commutative algebra is required.

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À propos de l'auteur

Jean-Luc Chabert, University of Picardie, France.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2026
Langue
anglais
ISBN 10 
1470482061
ISBN 13 
9781470482060
Reliure
Relié
Nombre de pages
314
Coordonnées du fabricant
non disponible
Personne responsable
non disponible