English

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.

Keywords

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

R2 v1 2026-06-21T08:57:05.257Z