Abhyankar's inequality

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Abhyankar's inequality is an inequality involving extensions of valued fields in algebra, introduced by Abhyankar (1956).

Abhyankar's inequality states that for an extension K/k of valued fields, the transcendence degree of K/k is at least the transcendence degree of the residue field extension plus the rank of the quotient of the valuation groups; here the rank of an abelian group [math]\displaystyle{ A }[/math] is defined as [math]\displaystyle{ \dim_{\mathbb{Q}}(A \otimes \mathbb{Q}) }[/math].

References