Characterizing Distinguished Pairs by Using Liftings of Irreducible Polynomials

Abstract

AbstractLet v be a henselian valuation of any rank of a field K and let be the unique extension of v to a fixed algebraic closure of K. In 2005, we studied properties of those pairs (θ,α) of elements of with where α is an element of smallest degree over K such thatSuch pairs are referred to as distinguished pairs. We use the concept of liftings of irreducible polynomials to give a different characterization of distinguished pairs.