On Saturated Distinguished Chains over a Local Field

Ota, Kaori

doi:10.1006/jnth.1999.2437

Cited by 13 publications

(15 citation statements)

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“…It may be pointed out that the above theorem generalizes Theorem 3.2 in [5] which is proved in the special case when (K, v) is a local field, i.e., a finite extension of the field of p-adic numbers or of F p ((T )). Our proof of this theorem is more or less self-contained.…”

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confidence: 84%

On Construction of Saturated Distinguished Chains

Singh

Khanduja

2007

Mathematika

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Abstract. Let v be a Henselian valuation of arbitrary rank of a field K andv be the (unique) extension of v to a fixed algebraic closure K of K.For an element α belonging to K\K, a chain α = α 0 , α 1 , ..., α r of elements of K such that α i is of minimum degree over K with the property thatThe 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 K (cf. [J. Number Theory, 52 (1995), 98-118.] and [J. Algebra, 266 (2003), 14-26]). In this paper, we describe a method of constructing a saturated distinguished chain for α and also determine 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 v.

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confidence: 84%

On Construction of Saturated Distinguished Chains

Singh

Khanduja

2007

Mathematika

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“…Several precise relations involving the chains D K (α) and N K (α) have been established by Ota in [5]. For instance, Theorem 3.2 and Proposition 3.4 of [5] imply that the chains D K (α) and N K (α) coincide if the characteristic of the residue field of…”

Section: (K B[t T] ∩ K)mentioning

confidence: 99%

“…For instance, Theorem 3.2 and Proposition 3.4 of [5] imply that the chains D K (α) and N K (α) coincide if the characteristic of the residue field of…”

Section: (K B[t T] ∩ K)mentioning

confidence: 99%

“…These chains D K (α) play an essential role in the description of the structure of irreducible polynomials over K. We mention in this context that they can also be defined in terms of the so-called saturated distinguished chains introduced in [6] and later studied also in [1] and [5]. In this paper we try to keep the presentation short and as self-contained as possible.…”

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confidence: 99%

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Chains of metric invariants over a local field

Popescu

Vâjâitu

et al. 2002

Acta Arith.

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“…This paper is a continuation of the paper [6] on saturated distinguished chains (SDCs) over a local field, where we showed that SDCs are closely related to the ramification theory. For a separable element over a local field K with ∈ K, a SDC for over K is a sequence ( , 1 , .…”

Section: Introductionmentioning

confidence: 96%

On saturated distinguished chains over a local field II

Ota

2005

Journal of Number Theory

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This is a continuation of the paper (J Number Theory 79 (1999) 217) on saturated distinguished chains (SDCs) over a local field K. Here, we give a "canonical" choice of the next element 1 in a SDC for = 1 + 1 considered in (Ota, 1999) for wildly totally ramified Galois extensions, and this leads us to consider a tower of fields, K ⊂ K 1 ⊂ K 2 ⊂ . . ., where K 1 = K( 1 ) and K n /K is wildly totally ramified. The union of these fields K = ∞ n=1 K n is particularly interesting, for its conductor over K is very small, close to 1. Moreover, in some cases K is uniquely determined up to isomorphism over K for any such extensions of the same type. We also consider SDCs for an element = 1 + 1 2 + · · · + 1 2 · · · n for totally ramified Galois extensions of type (m, m, ..., m), where m is a power of the characteristic of the residual field of K.

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On Saturated Distinguished Chains over a Local Field

Cited by 13 publications

References 3 publications

On Construction of Saturated Distinguished Chains

On Construction of Saturated Distinguished Chains

Chains of metric invariants over a local field

On saturated distinguished chains over a local field II

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