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= θ_{0}, θ_{1},...θ_{m}of elements of K̅ such that θ̅(θ_{i−1}−θ_{i})=SUP{ v̅(θ_{i−1}−β)|[K(β):K]<[K(θ_{i−1}):K]} and θ_{m} ∈ 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 |
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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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