Published online by Cambridge University Press: 30 October 2000
Ritt has shown that any complex polynomial p can be written as the composition of polynomials p1,…,pm, where each pj is prime in the sense that it cannot be written as a non-trivial composition of polynomials. The factors pj are not unique but the number m of them is, as is the set of the degrees of the pj. The paper extends Ritt's theory and, in particular, a third invariant of the decomposition is introduced.