A structure theorem for simple transcendental extensions of valued fields

Matignon, Michel; Ohm, Jack

doi:10.1090/S0002-9939-1988-0962804-0

A structure theorem for simple transcendental extensions of valued fields
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Proc. Amer. Math. Soc. 104 (1988), 392-402 Request permission

Abstract:

The fundamental inequality for a finite algebraic extension of a valued field relates the degree of the extension to the ramification indices and residue degrees, and of primary importance is the question of when this inequality becomes equality. An analogous question for simple transcendental extensions is treated here as an application of a fundamental structure theorem for such extensions.

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Modern algebra