Search

Your search keyword '"Absolutely irreducible"' showing total 2 results
Start Over Descriptor "Absolutely irreducible" Topic integer-valued polynomial
2 results on '"Absolutely irreducible"'

1. Strong atoms in monadically Krull monoids.

Author

Angermüller, Gerhard

Subjects
*ATOMS, *MONOIDS, *POLYNOMIAL rings
Abstract

It is shown that strong atoms are rather abundant in monadically Krull monoids. An application to rings of integer-valued polynomials on Krull domains yields new results on strong atoms in these rings. [ABSTRACT FROM AUTHOR]

Published
2022
Full Text
View/download PDF

2. Polynomial parametrization of the solutions of Diophantine equations of genus 0

Author

Sophie Frisch and Günter Lettl

Subjects
Integer-valued polynomial, 13F20, Pure mathematics, Polynomial, Mathematics - Number Theory, Absolutely irreducible, General Mathematics, Diophantine equation, Field (mathematics), Rational function, 11D85, 13F20, 11D41, 14H05, Commutative Algebra (math.AC), Mathematics - Commutative Algebra, 11D85, 11D41, Integer, polynomial parametrization, Homogeneous polynomial, FOS: Mathematics, 14H05, integer-valued polynomial, Number Theory (math.NT), resultant, Mathematics
Abstract

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 isomorphic to the rational function field Q(t). We show that all integral solutions of the Diophantine equation f=0 (up to those corresponding to some singular points) can be parametrized by a single triple of integer-valued polynomials. In general, it is not possible to parametrize this set of solutions by a single triple of polynomials with integer coefficients., Dedicated to Prof. W. Narkiewicz on the occasion of his 70th birthday. To appear in Functiones et Approximatio. 4 pages

Published
2008

Catalog

Books, media, physical & digital resources
See catalog results