Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals → CMB
Abstract view

# Characterizing Distinguished Pairs by Using Liftings of Irreducible Polynomials

 Read article[PDF: 621KB]
Published:2015-02-10
Printed: Jun 2015
• Kamal Aghigh,
Department of Mathematics, K. N. Toosi University of Technology, P.O.Box 16315-1618, Tehran, Iran
• Azadeh Nikseresht,
Department of Mathematics, K. N. Toosi University of Technology, P.O.Box 16315-1618, Tehran, Iran
 Format: LaTeX MathJax PDF

## 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.
 Keywords: valued fields, non-Archimedean valued fields, irreducible polynomials
 MSC Classifications: 12J10 - Valued fields 12J25 - Non-Archimedean valued fields [See also 30G06, 32P05, 46S10, 47S10] 12E05 - Polynomials (irreducibility, etc.)

 top of page | contact us | privacy | site map |

© Canadian Mathematical Society, 2018 : https://cms.math.ca/