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Integer-valued polynomials / Paul-Jean Cahen, Jean-Luc Chabert

Auteur principal : Cahen, Paul-Jean, 1946-, AuteurCo-auteur : Chabert, Jean-Luc, 1946-, AuteurType de document : MonographieCollection : Mathematical surveys and monographs, 48Langue : anglais.Pays : Etats Unis.Éditeur : Providence : American Mathematical Society, 1997Description : 1 vol. (xix-322 p.) ; 25 cmISBN : 9780821803882.ISSN : 0885-4653.Bibliographie : Bibliogr. p. [307]-316. Index.Sujet MSC : 13F20, Arithmetic rings and other special commutative rings, Polynomial rings and ideals; rings of integer-valued polynomials
13B25, Commutative ring extensions and related topics, Polynomials over commutative rings
11C08, Polynomials and matrices, Polynomials in number theory
11R09, Algebraic number theory: global fields, Polynomials (irreducibility, etc.)
13A15, General commutative ring theory, Ideals and multiplicative ideal theory in commutative rings
En-ligne : Zentralblatt | MathScinet | AMS
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Bibliogr. p. [307]-316. Index

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. (source : AMS)

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