Abhyankar's inequality

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

If K/k is an extension of valued fields, then Abhyankar's inequality states that the transcendence degree of K/k is at least the transcendence degree of the residue field extension plus the Q-rank of the quotient of the valuation groups.

References

• Abhyankar, Shreeram (1956), "On the valuations centered in a local domain", American Journal of Mathematics 78: 321–348, ISSN 0002-9327, JSTOR 2372519, MR 0082477