On dense sequences of polynomials in several variables

In the present paper a form of generalization of Gelfond's lemma on dense sequences of polynomials is proposed. For a set of complex numbers₁, ...,_s we define the coefficients_gk(₁, ...,_s) (0ks) and give the relations between them and the transcendental degrees or the transcendence types of the field © (₁, ...,_s) or its subfields.This work was completed at the Dept. of Math., Univ. of Southern Mississippi, USA in 1987.