On chains associated with elements algebraic over a henselian valued field

Aghigh, Kamal ; Khanduja, Sudesh K. (2005) On chains associated with elements algebraic over a henselian valued field Algebra Colloquium (AC), 12 (4). pp. 607-616. ISSN 1005-3867

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Official URL: http://www.worldscinet.com/ac/12/1204/S10053867050...

Abstract

Let v be a henselian valuation of a field K,and v̅ be the (unique) extension of v to a fixed algebraic closure of K̅. For an element θ∈K̅\K, a chain θ= θ0, θ1,...θmof elements of K̅ such that θ̅(θi−1−θi)=SUP{ v̅(θi−1−β)|[K(β):K]<[K(θi−1):K]} and θm ∈ K, is called a complete distinguished chain for θ with respect to (K, v). In 1995, Popescu and Zaharescu proved the existence of a complete distinguished chain for each θ∈K̅\K when (K, v) is a complete discrete rank one valued field (cf. [10]). In this paper, for a henselian valued field (K, v) of arbitrary rank, we characterize those elements θ∈K̅\K for which there exists a complete distinguished chain. It is shown that a complete distinguished chain for θ gives rise to several invariants associated to θ which are same for all the K-conjugates of θ.

Item Type:Article
Source:Copyright of this article belongs to World Scientific Publishing.
Keywords:Valued Fields; Non-archimedean Valued Fields; Valuations and their Generalizations
ID Code:69879
Deposited On:19 Nov 2011 11:10
Last Modified:19 Nov 2011 11:10

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