Abstract view
Characterizing Distinguished Pairs by Using Liftings of Irreducible Polynomials


Published:20150210
Printed: Jun 2015
Kamal Aghigh,
Department of Mathematics, K. N. Toosi University of Technology, P.O.Box 163151618, Tehran, Iran
Azadeh Nikseresht,
Department of Mathematics, K. N. Toosi University of Technology, P.O.Box 163151618, Tehran, Iran
Abstract
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.
MSC Classifications: 
12J10, 12J25, 12E05 show english descriptions
Valued fields NonArchimedean valued fields [See also 30G06, 32P05, 46S10, 47S10] Polynomials (irreducibility, etc.)
12J10  Valued fields 12J25  NonArchimedean valued fields [See also 30G06, 32P05, 46S10, 47S10] 12E05  Polynomials (irreducibility, etc.)
