Abhyankar's inequality

Abhyankar's inequality is an inequality involving extensions of valued fields in algebra, introduced by Template:Harvs.

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 $A$ is defined as ${\dim }_{\mathbb{Q}}(A\otimes \mathbb{Q})$.

References

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