Metric invariants over Henselian valued fields

Angel Popescu, Nicolae Popescu, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
Pages (from-to)14-26
Number of pages13
JournalJournal of Algebra
Volume266
Issue number1
DOIs
StatePublished - Aug 1 2003

Keywords

  • Henselian fields
  • Metric invariants
  • Valued fields

ASJC Scopus subject areas

  • Algebra and Number Theory

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