Amrit Pal, Dr. ; Khanduja, Sudesh K.
(2007)
*On construction of saturated distinguished chains*
Mathematika, 54
(1-2).
pp. 59-65.
ISSN 0025-5793

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Official URL: http://journals.cambridge.org/action/displayAbstra...

Related URL: http://dx.doi.org/10.1112/S0025579300000218

## Abstract

Let υ be a Henselian valuation of arbitrary rank of a field K, and let ῡ be the (unique) extension of v to a fixed algebraic closure K̅of K. For an element α ε K̅\K, a chain α = α_{0}, α_{1},…,α_{r} of elements of K̅,such that α_{i} is of minimum degree over K with the property that ῡ(α_{i-1}-α_{i})= sup{ῡ(α_{i-1}-β)|[K(β): K] < [K(α_{i}-1):K]} and that α_{r} ε K , is called a saturated distinguished chain for α with respect to (K, υ). The notion of a saturated distinguished chain has been used to obtain results about the irreducible polynomials over any complete discrete rank one valued field K and to determine various arithmetic and metric invariants associated to elements of K̅(cf. [J. Number Theory, 52 (1995), 98–118.] and [J. Algebra, 266 (2003), 14–26]). In this paper, a method is described of constructing a saturated distinguished chain for α, and also determining explicitly some invariants associated to α, when the degree of the extension K (α)/K is not divisible by the characteristic of the residue field of υ.

Item Type: | Article |
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ID Code: | 69949 |

Deposited On: | 19 Nov 2011 11:13 |

Last Modified: | 19 Nov 2011 11:13 |

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