Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 33, No. 1, pp. 1-13 (2017)

On a sufficient and necessary condition for a multivariate polynomial to have algebraically dependent roots - an elementary proof

Csaba Vincze and Adrienn Varga

University of Debrecen

Abstract: In the paper we prove that a multivariate polynomial has algebraically dependent roots iff the coefficients are algebraic numbers up to a common proportional term. Here we present an elementary proof involving cardinality properties and basic linear algebra.

Keywords: Algebraic dependent systems, algebraic conjugates, Vandermonde matrix

Classification (MSC2000): 12D10; 39B22

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