Reducibility of polynomials in several variables. II

Andrzej Schinzel

Vol. 118 (1985), No. 2, 531–563

DOI: 10.2140/pjm.1985.118.531

Abstract

Let f_i(x_i) be non-constant rational functions over a field K (i = 1,2,…,n). A necessary and sufficient condition is given for reducibility over K of the numerator of the sum ∑ _i=1ⁿf_i(x_i) in its reduced form, provided n ≥ 3. In particular the numerator is irreducible if char K = 0, which generalizes a theorem of Ehrenfeucht and Pełczyński and answers a question of M. Jarden.

Mathematical Subject Classification 2000

Primary: 12E05

Milestones

Received: 2 May 1984

Revised: 10 September 1984

Published: 1 June 1985