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1. CMB 2015 (vol 58 pp. 225)

 Characterizing Distinguished Pairs by Using Liftings of Irreducible Polynomials Let $v$ be a henselian valuation of any rank of a field $K$ and $\overline{v}$ be the unique extension of $v$ to a fixed algebraic closure $\overline{K}$ of $K$. In 2005, it was studied properties of those pairs $(\theta,\alpha)$ of elements of $\overline{K}$ with $[K(\theta): K]\gt [K(\alpha): K]$ where $\alpha$ is an element of smallest degree over $K$ such that $$\overline{v}(\theta-\alpha)=\sup\{\overline{v}(\theta-\beta) |\ \beta\in \overline{K}, \ [K(\beta): K]\lt [K(\theta): K]\}.$$ Such pairs are referred to as distinguished pairs. We use the concept of liftings of irreducible polynomials to give a different characterization of distinguished pairs. Keywords:valued fields, non-Archimedean valued fields, irreducible polynomialsCategories:12J10, 12J25, 12E05