Characterizing Distinguished Pairs by Using Liftings of Irreducible Polynomials

Canadian mathematical bulletin

Azadeh Nikseresht¹  Kamal Aghigh¹ 

[1] Department of Mathematics, K. N. Toosi University of Technology, P.O.Box 16315-1618, Tehran, Iran

关键词: valued fields;    non-Archimedean valued fields;    irreducible polynomials;   

DOI  :  10.4153/CMB-2014-064-2

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $v$ be a henselian valuation of any rank of a field$K$ and $overline{v}$ be the unique extension of $v$ to afixed algebraic closure $overline{K}$ of $K$. In 2005, it was studied propertiesof those pairs $(heta,alpha)$ of elements of $overline{K}$with $[K(heta): K]gt [K(alpha): K]$ where $alpha$ is an elementof smallest degree over $K$ such that$$overline{v}(heta-alpha)=sup{overline{v}(heta-eta)| etain overline{K},[K(eta): K]lt [K(heta): K]}.$$Such pairs are referred to as distinguished pairs.We use the concept of liftings of irreducible polynomials to give adifferent characterization of distinguished pairs.

【 授权许可】

Unknown