On the generalized difference polynomials
Factorization properties of a class of polynomials F in two indeterminates with the coefficients in an algebraically closed field are investigated. This class includes the generalized difference polynomials considered by \textit{L. A. Rubel} and \textit{S. S. Abhyankar} [J. Indian Math. Soc., New Ser. 43, 69-78 (1979; Zbl 0532.12021)] and by \textit{L. A. Rubel}, \textit{A. Schinzel} and \textit{H. Tverberg} [J. Number Theory 12, 230-235 (1980; Zbl 0435.12009)]. A rational number \(p_ Y(F)\) associated with the polynomial \(F\in k[X,Y]\) is introduced and some properties of \(p_ Y(F)\) using a Newton polygon argument are established. New irreducibility criteria for polynomials in two variables with the coefficients in an algebraically closed field are deduced and new proofs for the irreducibility criteria of A. Ehrenfeucht and G. Angermüller are obtained.
scientific article; zbMATH DE number 4128944