On a criterion for algebraic independence and its variants
Abstract
From around 2010 onward, Elsner et al.,developed and applied a method in which the algebraic independence of n quantities x1,...,xn over a field is transferred to further n quantities y1,...,yn by means of a system of polynomials in 2n variables X1,...,Xn,Y1,...,Yn. In this paper, we systematically study and explain this criterion and its variants.
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