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Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 33, No. 1, pp. 1-13 (2017)
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On a sufficient and necessary condition for a multivariate polynomial to have algebraically dependent roots - an elementary proof

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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

**Full text of the article:**

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FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition
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