پولینوم‌های با مقادیر صحیح (بررسی‌ها و مونوگرافی‌های ریاضی)

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. Integer-valued Polynomials On The Ring Of Integers Have Been Known For A Long Time And Have Been Used In Calculus. P @olya 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 Righ Structure, And The Very Numerous Questions It Raises Allow A Throrough Exploration Of Commuative Algebra. Here Is The First Book Devoted Entirely To This Topic. Features: Bl Thorough Reviews Of Many Published Works Bl Self-contained Text With Complete Proofs Bl Numerous Exercises 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. 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. This book addresses this topic.