Sophie Frisch

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Every function on a nite residue class ring D=I of a Dedekind domain D is induced by an integer-valued polynomial on D that preserves congruences mod I if and only if I is a power of a prime ideal. If R is a nite commutative local ring with maximal ideal P of nilpotency N satisfying for all a; b 2 R, if ab 2 Pn then a 2 P k , b 2 P j with k + j min(n;N), we(More)
We show that for a wide variety of domains, including all Dedekind rings with finite residue fields, it is possible to separate any two algebraic elements a, b of an algebra over the quotient field by integer-valued polynomials (i.e. to map a and b to 0 and 1, respectively, with a polynomial in K[x] that maps every element of D to an element of D), provided(More)
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(More)
For an arbitrary finite set S of natural numbers greater 1, we construct f ∈ Int(Z)= {g∈Q[x] | g(Z)⊆Z} such that S is the set of lengths of f , i.e., the set of all n such that f has a factorization as a product of n irreducibles in Int(Z). More generally, we can realize any finite multi-set of natural numbers greater 1 as the multi-set of lengths of the(More)
If R is a subring of a Krull ring S such that RQ is a valuation ring for every finite index Q = P ∩ R, P in Spec1(S), we construct polynomials that map R into the maximal possible (for a monic polynomial of fixed degree) power of PSP , for all P in Spec 1(S) simultaneously. This gives a direct sum decomposition of Int(R, S), the S-module of polynomials with(More)
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(More)
We investigate non-unique factorization of polynomials in Zpn [x] into irreducibles. As a Noetherian ring whose zero-divisors are contained in the Jacobson radical, Zpn [x] is atomic. We reduce the question of factoring arbitrary non-zero polynomials into irreducibles to the problem of factoring monic polynomials into monic irreducibles. The multiplicative(More)