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Integer-Valued Polynomials, PDF eBook

Integer-Valued Polynomials PDF

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Description

Integer-valued polynomials on the ring of integers have been known for a long time and have been used in calculus.

Polya 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.

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