Algebraic function field

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In mathematics, an algebraic function field (often abbreviated as function field) of n variables over a field k is a finitely generated field extension K/k which has transcendence degree n over k.^[1] Equivalently, an algebraic function field of n variables over k may be defined as a finite field extension of the field K = k(x₁,...,x_n) of rational functions in n variables over k.