On Algebraically Maximal Valued Fields and Defectless Extensions

Bishnoi, Anuj; Khanduja, Sudesh K.

doi:10.4153/cmb-2011-148-0

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Cited by 4 publications

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“…The maximum of M (a), whenever it exists, is denoted by δ(a, K). It has been shown in Theorem 1.3 of [6] that M (a) admits a maximum whenever (K(a)|K, ν) is a defectless extension. A pair (a, z)…”

Section: Consider the Setmentioning

confidence: 99%

Minimal pairs, minimal fields and implicit constant fields

Dutta¹

2021

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Minimal pairs of definition were introduced by Alexandru, Popescu and Zaharescu [3,4,5] to study residue transcendental extensions. In this paper we obtain analogous results in the value transcendental case. We introduce the notion of minimal fields of definition for valuation transcendental extensions and show that they share some common ramification theoretic properties. The connection between minimal fields of definition and implicit constant fields is also investigated. Further, we explore the relationship between valuation transcendental extensions and pseudo-Cauchy sequences.

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Section: Consider the Setmentioning

confidence: 99%