eBook ISBN:  9781470412791 
Product Code:  SURV/48.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9781470412791 
Product Code:  SURV/48.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsMathematical Surveys and MonographsVolume: 48; 1997; 322 ppMSC: Primary 13; Secondary 11
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 \(D\)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.
 Selfcontained text with complete proofs.
 Numerous exercises.
ReadershipGraduate students and research mathematicians interested in commutative algebra and algebraic number theory.

Table of Contents

Chapters

I. Coefficients and values

II. Additive structure

III. StoneWeierstrass

IV. Integervalued polynomials on a subset

V. Prime ideals

VI. Multiplicative properties

VII. Skolem properties

VIII. Invertible ideals and the Picard group

IX. Integervalued derivatives and finite differences

X. Integervalued rational functions

XI. Integervalued polynomials in several indeterminates


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


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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 \(D\)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.
 Selfcontained text with complete proofs.
 Numerous exercises.
Graduate students and research mathematicians interested in commutative algebra and algebraic number theory.

Chapters

I. Coefficients and values

II. Additive structure

III. StoneWeierstrass

IV. Integervalued polynomials on a subset

V. Prime ideals

VI. Multiplicative properties

VII. Skolem properties

VIII. Invertible ideals and the Picard group

IX. Integervalued derivatives and finite differences

X. Integervalued rational functions

XI. Integervalued polynomials in several indeterminates

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