Polynomials with a common composite
Algebraic Geometry
2013-10-08 v2 Number Theory
Abstract
Let f and g be nonconstant polynomials over an arbitrary field K. In this paper we study the intersection of the polynomial rings K[f] and K[g], and in particular we ask whether this intersection is larger than K. We completely resolve this question when K has characteristic zero, and in positive characteristic we present various results, examples, and algorithms.
Cite
@article{arxiv.0707.1552,
title = {Polynomials with a common composite},
author = {Robert M. Beals and Joseph L. Wetherell and Michael E. Zieve},
journal= {arXiv preprint arXiv:0707.1552},
year = {2013}
}
Comments
20 pages; various minor changes, and some alternate proofs suggested by the referee