Integer-Valued Polynomials and Prüfer v-Multiplication Domains
نویسندگان
چکیده
منابع مشابه
Generalizations of Dedekind domains and integer-valued polynomials
This talk will provide a snapshot of contemporary commutative algebra. In classical commutative algebra and algebraic number theory, the Dedekind domains are the most important class of rings. Modern commutative algebra studies numerous generalizations of the Dedekind domains in attempts to generalize results of algebraic number theory. This talk will introduce a few important generalizations o...
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Let D be a domain with quotient field K and A a D-algebra. A polynomial with coefficients in K that maps every element of A to an element of A is called integer-valued on A. For commutative A we also consider integer-valued polynomials in several variables. For an arbitrary domain D and I an arbitrary ideal of D we show I -adic continuity of integer-valued polynomials on A. For Noetherian one-d...
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Every integer is either even or odd, so we know that the polynomial f(x) = x(x− 1) 2 is integervalued on the integers, even though its coefficients are not in Z. Similarly, since every binomial coefficient ( k n ) is an integer, the polynomial ( x n ) = x(x− 1)...(x− n+ 1) n! must also be integervalued. These polynomials were used for polynomial interpolation as far back as the 17 century. Inte...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2000
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.8155