Kumar, Munish ; Khanduja, Sudesh K.
(2006)
*A formula for Tignol's constant*
Journal of Algebra, 305
(1).
pp. 603-613.
ISSN 0021-8693

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/j.jalgebra.2006.01.016

## Abstract

Let (K, v) be a Henselian valued field and (L,w) be a finite separable extension of (K, v). In
2004, it was proved that the set A_{L/K} defined by A_{L/K} = {v(Tr_{L/K}(α)) − w(α) | α ∈ L, α ≠ = 0} has a minimum element if and only if [L : K] = ef where e,f are the ramification index and the
residual degree of w/v, i.e., (L,w)/(K, v) is defectless. The constant minAL/K was first introduced
by Tignol and is referred to as Tignol’s constant. In 2005, K. Ota and Khanduja gave a formula for
minAL/K when (L,w)/(K, v) is an extension of local fields. In this paper, we give this formula
when (L,w) is any finite separable defectless extension of a Henselian valued field of arbitrary rank
and thereby generalize some well-known results of Dedekind regarding “different” of extensions of
algebraic number fields and ramification of prime ideals.

Item Type: | Article |
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Source: | Copyright of this article belongs to Elsevier Science. |

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

ID Code: | 69899 |

Deposited On: | 19 Nov 2011 11:13 |

Last Modified: | 19 Nov 2011 11:13 |

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