A formula for Tignol's constant

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


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 AL/K defined by AL/K = {v(TrL/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
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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