On page 211, line 9, and on page 213, line -6, the assumption should be added that F is not the product of generalized cyclotomic polynomials.
@article{bwmeta1.element.bwnjournal-article-aav60i4p417bwm,
author = {A. Bazylewicz},
title = {Corrigendum to the paper "An extension of a result of C. J. Smyth to polynomials in several variables" Acta Arith. 50 (1988), 211-214},
journal = {Acta Arithmetica},
volume = {62},
year = {1992},
pages = {417},
zbl = {0642.12006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav60i4p417bwm}
}
A. Bazylewicz. Corrigendum to the paper "An extension of a result of C. J. Smyth to polynomials in several variables" Acta Arith. 50 (1988), 211-214. Acta Arithmetica, Tome 62 (1992) p. 417. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav60i4p417bwm/