Polynomial decomposition
Mike Zieve
We consider the operation of composition on univariate polynomials over a field
K. If K has characteristic zero, Ritt (1921) showed precisely the extent of
non-uniqueness of the decomposition of a polynomial into indecomposable polynomials. After
reviewing Ritt's results, I will discuss new results and examples in the much more
complicated situation of positive characteristic. I will also discuss the related
question of when two subfields of a function field intersect in more than just constants.