39 citations · 144 across the 16 of their papers we have counts for
20 papers
P-adic approximation of algebraic integers and residue class rings of rings of integer-valued polynomials
Sophie Frisch, Franz Halter-Koch
Let F:K be a Galois extension of number fields and Q a prime ideal of O_F lying over the prime P of O_K. By analyzing the Q-adic closure of O_K in O_F we characterize those rings o…
Primes and absolutely or non-absolutely irreducible elements in atomic domains
Victor Fadinger, Sophie Frisch, Sarah Nakato +2
We give examples of atomic integral domains satisfying each of the eight logically possible combinations of existence or non-existence of the following kinds of elements: 1) primes…
Integer-valued polynomials on discrete valuation rings of global fields with prescribed lengths of factorizations
Victor Fadinger, Sophie Frisch, Daniel Windisch
Let be a valuation ring of a global field . We show that for all positive integers and there exists an integer-valued polynomial on , t…
Split absolutely irreducible integer-valued polynomials over discrete valuation domains
Sophie Frisch, Sarah Nakato, Roswitha Rissner
Regarding non-unique factorization of integer-valued polynomials over a discrete valuation domain with finite residue field, it is known that there exist absolutely irreduc…
Prime ideals in infinite products of commutative rings
Carmelo A. Finocchiaro, Sophie Frisch, Daniel Windisch
We describe the prime ideals and, in particular, the maximal ideals in products of families of commutative rings. We show that every maximal ideal…
A graph-theoretic criterion for absolute irreducibility of integer-valued polynomials with square-free denominator
Sophie Frisch, Sarah Nakato
An irreducible element of a commutative ring is absolutely irreducible if no power of it has more than one (essentially different) factorization into irreducibles. In the case of t…
Polynomial functions on rings of dual numbers over residue class rings of the integers
H. Al-Ezeh, A. A. Al-Maktry, S. Frisch
The ring of dual numbers over a ring is , where denotes . For any finite commutative ring , we characterize null polynomials and permutation…
Polynomial functions on non-commutative rings - a link between ringsets and null-ideal sets
Sophie Frisch
Regarding polynomial functions on a subset of a non-commutative ring , that is, functions induced by polynomials in (whose variable commutes with the coefficients), w…
Sets of lengths of factorizations of integer-valued polynomials on Dedekind domains with finite residue fields
Sophie Frisch, Sarah Nakato, Roswitha Rissner
Let be a Dedekind domain with infinitely many maximal ideals, all of finite index, and its quotient field. Let …
Polynomial functions on upper triangular matrix algebras
Sophie Frisch
There are two kinds of polynomial functions on matrix algebras over commutative rings: those induced by polynomials with coefficients in the algebra itself and those induced by pol…
On the spectrum of rings of functions
Sophie Frisch
Let be a domain and a maximal ideal of . The ring of integer-valued polynomials on a subset of , as well as more general rings of functions from to , can b…
Relative polynomial closure and monadically Krull monoids of integer-valued polynomials
Sophie Frisch
Let D be a Krull domain and Int(D) the ring of integer-valued polynomials on D. For any f in Int(D), we explicitly construct a divisor homomorphism from [f], the divisor-closed sub…
Integer-valued polynomials on algebras
Sophie Frisch
Let D be a domain with quotient field K and A a D-algebra. We call a polynomial with coefficients in K that maps every element of A to an element of A "integer-valued on A". For co…
A construction of integer-valued polynomials with prescribed sets of lengths of factorizations
Sophie Frisch
For an arbitrary finite set S of natural numbers greater 1, we construct an integer-valued polynomial f, whose set of lengths in Int(Z) is S. The set of lengths of f is the set of…
Sylow -groups of polynomial permutations on the integers mod
Sophie Frisch, Daniel Krenn
We describe the Sylow -groups of the group of polynomial permutations of the integers mod .
Polynomial parametrization of Pythagorean quadruples, quintuples and sextuples
Sophie Frisch, Leonid Vaserstein
A Pythagorean n-tuple is an integer solution of x_1^2+...+x_{n-1}^2=x_n^2. For n=4 and n=6, the Pythagorean n-tuples admit a parametrization by a single n-tuple of polynomials with…
Non-unique factorization of polynomials over residue class rings of the integers
Christopher Frei, Sophie Frisch
We investigate non-unique factorization of polynomials in Z_{p^n}[x] into irreducibles. As a Noetherian ring whose zero-divisors are contained in the Jacobson radical, Z_{p^n}[x] i…
Polynomial parametrization of the solutions of Diophantine equations of genus 0
Sophie Frisch, Günter Lettl
Let f in Z[X,Y,Z] be a non-constant, absolutely irreducible, homogeneous polynomial with integer coefficients, such that the projective curve given by f=0 has a function field isom…
Remarks on polynomial parametrization of sets of integer points
Sophie Frisch
If, for a subset S of Z^k, we compare the conditions of being parametrizable (a) by a single k-tuple of polynomials with integer coefficients, (b) by a single k-tuple of integer-va…
Parametrization of Pythagorean triples by a single triple of polynomials
Sophie Frisch, Leonid Vaserstein
It is well known that Pythagorean triples can be parametrized by two triples of polynomials with integer coefficients. We show that no single triple of polynomials with integer coe…