A generalization of Ehrenfeucht's irreducibility criterion

Abstract

Listen

Translate article

For polynomials of the form Q = P( f( X), g( Y), where P is a generalized difference polynomial and f, g are polynomials in several variables, we prove a sufficient criterion for irreducibility. Moreover, we show that (in characteristic 0) any two non-constant factors of Q cannot generate the unit ideal in the polynomial ring with variables X, Y.