Polynomials with a common composite
Robert M. Beals, Joseph L. Wetherell, Michael E. Zieve · arXiv (Cornell University) · 2007
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.