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...
متن کاملInteger-valued Polynomials
Let R be a Krull ring with quotient field K and a1, . . . , an in R. If and only if the ai are pairwise incongruent mod every height 1 prime ideal of infinite index in R does there exist for all values b1, . . . , bn in R an interpolating integer-valued polynomial, i.e., an f ∈ K[x] with f(ai) = bi and f(R) ⊆ R. If S is an infinite subring of a discrete valuation ring Rv with quotient field K a...
متن کاملInteger-valued Polynomials on Algebras
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...
متن کاملWhat are Rings of Integer-Valued Polynomials?
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...
متن کاملGeneralized Rings of Integer-valued Polynomials
The classical ring of integer-valued polynomials Int(Z) consists of the polynomials in Q[X] that map Z into Z. We consider a generalization of integervalued polynomials where elements of Q[X] act on sets such as rings of algebraic integers or the ring of n× n matrices with entries in Z. The collection of polynomials thus produced is a subring of Int(Z), and the principal question we consider is...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2000
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(99)00073-0