Abstract
In this paper we generalize the notion of a saturated distinguished sequence associated to a separable element a ∈ K̄, over a local field K [J. Number Theory 79 (1999) 217; J. Number Theory 52 (1995) 98] to the case of an arbitrary Henselian field (K, v). We use these distinguished sequences to study various arithmetic and metric invariants of a, generalizing some results from [J. Math. Kyoto Univ. 30 (1990) 207; J. Number Theory 79 (1999) 217; A. Popescu, N. Popescu, M. Vâjâitu, A. Zacharescu, Chains of metric invariants over p-adic fields, Acta Arith., to appear; J. Number Theory 52 (1995) 98; Portugal. Math. 54 (1997) 73]. In the process we also obtain some Ax-Sen type inequalities (see [J. Algebra 15 (1970) 417; Ann. of Math. 90 (1969) 33]).
Original language | English (US) |
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Pages (from-to) | 14-26 |
Number of pages | 13 |
Journal | Journal of Algebra |
Volume | 266 |
Issue number | 1 |
DOIs | |
State | Published - Aug 1 2003 |
Keywords
- Henselian fields
- Metric invariants
- Valued fields
ASJC Scopus subject areas
- Algebra and Number Theory