Irreducibility results for compositions of polynomials with integer coefficients (Q867144)

The paper begins by a very interesting survey of results on irreducibility of composite polynomials. In this work, the authors obtain explicit upper bounds for the number of irreducible factors for a class of polynomials of the form \(f \circ g\), where \(f\) and \(g\) are polynomials with integer coefficients, in terms of the degrees of \(f\) and \(g\), and the size of the coefficients of \(f\). In particular, some irreducibility results are given for this class of composite polynomials. The methods of proofs are essentially elementary.