Characterizing Distinguished Pairs by Using Liftings of Irreducible Polynomials

摘要

Let v be a henselian valuation of any rank of a field K and let (v) over bar be the unique extension of v to a fixed algebraic closure (K) over bar of K. In 2005, we studied properties of those pairs (theta, alpha) of elements of (K) over bar with [K(theta): K] > [K(alpha):K] where alpha is an element of smallest degree over K such that