On the uniqueness of maximal immediate extensions of valued differential fields

Lou van den Dries, Nigel Pynn-Coates

Research output: Contribution to journalArticle

Abstract

So far there exist just a few results about the uniqueness of maximal immediate valued differential field extensions and about the relationship between differential-algebraic maximality and differential-henselianity; see [1, Chapter 7]. We remove here the assumption of monotonicity in these results but replace it with the assumption that the value group is the union of its convex subgroups of finite (archimedean) rank. We also show the existence and uniqueness of differential-henselizations of asymptotic fields with such a value group.

Original languageEnglish (US)
Pages (from-to)87-100
Number of pages14
JournalJournal of Algebra
Volume519
DOIs
StatePublished - Feb 1 2019

Fingerprint

Uniqueness
Field extension
Monotonicity
Union
Existence and Uniqueness
Subgroup

Keywords

  • Differential-henselianity
  • Differential-henselizations
  • Finite archimedean rank
  • Valued differential fields

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

On the uniqueness of maximal immediate extensions of valued differential fields. / van den Dries, Lou; Pynn-Coates, Nigel.

In: Journal of Algebra, Vol. 519, 01.02.2019, p. 87-100.

Research output: Contribution to journalArticle

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