Bhatia, Saurabh ; Khanduja, Sudesh K.
(2005)
*On limits of sequences of algebraic elements over a complete field*
Algebra Colloquium, 12
(4).
pp. 617-628.
ISSN 1005-3867

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

## Abstract

Let K be a complete field with respect to a real non-trivial valuation v, and ν̅be the extension of v to an algebraic closure K̅ of K. A well-known result of Ostrowski asserts that the limit of a Cauchy sequence of elements of K̅ does not always belong to K̅ unless K̅is a finite extension of K. In this paper, it is shown that when a Cauchy sequence { b_{n}} of elements of K̅ is such that the sequence { [K(b_{n}): K] } of degrees of the extensions K(b_{n})/K does not tend to infinity as n approaches infinity, then {b_{n}}has a limit in K̅.We also give a characterization of those Cauchy sequences {b_{n}} of elements of K̅whose limit is not in K̅,which generalizes a result of Alexandru, Popescu and Zaharescu.

Item Type: | Article |
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Source: | Copyright of this article belongs to World Scientific Publishing Company. |

Keywords: | Valued Fields; Non-Archimedean Valued Fields; Completions |

ID Code: | 69947 |

Deposited On: | 19 Nov 2011 11:11 |

Last Modified: | 19 Nov 2011 11:11 |

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