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

Vincze, Csaba and Vámosiné Varga, Adrienn (2017) On a sufficient and necessary condition for a multivariate polynomial to have algebraically dependent roots - an elementary proof. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 33 (1). pp. 1-13. ISSN 0866-0174

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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.

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