Mathematical Surveys and Monographs 1997; 322 pp; hardcover Volume: 48 ISBN10: 0821803883 ISBN13: 9780821803882 List Price: US$96 Member Price: US$76.80 Order Code: SURV/48
 Integervalued 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 \(D\)algebrathat 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.
 Selfcontained 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 integervalued 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
 StoneWeierstrass
 Integervalued polynomials on a subset
 Prime ideals
 Multiplicative properties
 Skolem properties
 Invertible ideals and the Picard group
 Integervalued derivatives and finite differences
 Integervalued rational functions
 Integervalued polynomials in several indeterminates
 References
 List of symbols
 Index
