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Integer-Valued Polynomials
Paul-Jean Cahen and Jean-Luc Chabert, Faculté de Science de St Jerome, Marseille, France
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Mathematical Surveys and Monographs
1997; 322 pp; hardcover
Volume: 48
ISBN-10: 0-8218-0388-3
ISBN-13: 978-0-8218-0388-2
List Price: US$91
Member Price: US$72.80
Order Code: SURV/48
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Integer-valued polynomials on the ring of integers have been known for a long time and have been used in calculus. Pólya and Ostrowski generalized this notion to rings of integers of number fields. More generally still, one may consider a domain \(D\) and the polynomials (with coefficients in its quotient field) mapping \(D\) into itself. They form a \(D\)-algebra--that is, a \(D\)-module with a ring structure. Appearing in a very natural fashion, this ring possesses quite a rich structure, and the very numerous questions it raises allow a thorough exploration of commutative algebra. Here is the first book devoted entirely to this topic.

Features:

  • Thorough reviews of many published works.
  • Self-contained text with complete proofs.
  • Numerous exercises.

Readership

Graduate students and research mathematicians interested in commutative algebra and algebraic number theory.

Reviews

"Begins with two interesting introductions (both historical and mathematical) and includes almost 300 exercises ... this makes the text not only a volume for experts, but usable in a classroom setting. Its bibliography ... is by far the most extensive on this subject ... an excellent book for readers new to the subject. For readers familiar with the field, it will be the key reference for many years to come."

-- Mathematical Reviews

"The authors succeeded in presenting everything of importance in the theory of integer-valued polynomials and this short review cannot do justice to the rich contents of their book. The presentation of the material is very good and the book offers a pleasant reading."

-- Zentralblatt MATH

Table of Contents

  • Coefficients and values
  • Additive structure
  • Stone-Weierstrass
  • Integer-valued polynomials on a subset
  • Prime ideals
  • Multiplicative properties
  • Skolem properties
  • Invertible ideals and the Picard group
  • Integer-valued derivatives and finite differences
  • Integer-valued rational functions
  • Integer-valued polynomials in several indeterminates
  • References
  • List of symbols
  • Index
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