Polynomials with a common composite

Details Polynomials with a common composite Polynomials with a common composite

2007-07-11

arxiv.org/abs/0707.1552v2

Mathematics

Algebraic Geometry

20 pages; various minor changes, and some alternate proofs suggested by the referee

Scientific paper

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.

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