Towers of complements to valuation rings and truncation closed embeddings of valued fields

No Thumbnail Available
Files
There are no files associated with this item.
Date
2010
Authors
Fornasiero, Antongiulio
Kuhlmann, Franz-Viktor
Editors
Contact
Journal ISSN
Electronic ISSN
ISBN
Bibliographical data
Publisher
Series
URI (citable link)
ArXiv-ID
International patent number
Link to the license
EU project number
Project
Open Access publication
Restricted until
Title in another language
Research Projects
Organizational Units
Journal Issue
Publication type
Journal article
Publication status
Published in
Journal of Algebra ; 323 (2010), 3. - pp. 574-600. - ISSN 0021-8693
Abstract
We study necessary and sufficient conditions for a valued field K with value group G and residue field k (with char K=char k) to admit a truncation closed embedding in the field of generalized power series k((G,f)) (with factor set f). We show that this is equivalent to the existence of a family (tower of complements) of k-subspaces of K which are complements of the (possibly fractional) ideals of the valuation ring, and satisfying certain natural conditions. If K is a Henselian field of characteristic 0 or, more generally, an algebraically maximal Kaplansky field, we give an intrinsic construction of such a family which does not rely on a given truncation closed embedding. We also show that towers of complements and truncation closed embeddings can be extended from an arbitrary field to at least one of its maximal immediate extensions.
Summary in another language
Subject (DDC)
510 Mathematics
Keywords
Completion of an ordered group,Valued field,Fields of generalized power series,Truncation closed embedding,Complement to valuation ring
Conference
Review
undefined / . - undefined, undefined. - (undefined; undefined)
Cite This
ISO 690FORNASIERO, Antongiulio, Franz-Viktor KUHLMANN, Salma KUHLMANN, 2010. Towers of complements to valuation rings and truncation closed embeddings of valued fields. In: Journal of Algebra. 323(3), pp. 574-600. ISSN 0021-8693. Available under: doi: 10.1016/j.jalgebra.2009.11.023
BibTex
@article{Fornasiero2010Tower-12753,
  year={2010},
  doi={10.1016/j.jalgebra.2009.11.023},
  title={Towers of complements to valuation rings and truncation closed embeddings of valued fields},
  number={3},
  volume={323},
  issn={0021-8693},
  journal={Journal of Algebra},
  pages={574--600},
  author={Fornasiero, Antongiulio and Kuhlmann, Franz-Viktor and Kuhlmann, Salma}
}
RDF
<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/12753">
    <dc:contributor>Fornasiero, Antongiulio</dc:contributor>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dcterms:title>Towers of complements to valuation rings and truncation closed embeddings of valued fields</dcterms:title>
    <dc:creator>Kuhlmann, Franz-Viktor</dc:creator>
    <dc:rights>terms-of-use</dc:rights>
    <dc:contributor>Kuhlmann, Franz-Viktor</dc:contributor>
    <dcterms:issued>2010</dcterms:issued>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-07-15T08:51:12Z</dcterms:available>
    <dc:creator>Kuhlmann, Salma</dc:creator>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/12753"/>
    <dcterms:bibliographicCitation>First publ. in: Journal of Algebra 323 (2010), 3, pp. 574-600</dcterms:bibliographicCitation>
    <dcterms:abstract xml:lang="eng">We study necessary and sufficient conditions for a valued field K with value group G and residue field k (with char K=char k) to admit a truncation closed embedding in the field of generalized power series k((G,f)) (with factor set f). We show that this is equivalent to the existence of a family (tower of complements) of k-subspaces of K which are complements of the (possibly fractional) ideals of the valuation ring, and satisfying certain natural conditions. If K is a Henselian field of characteristic 0 or, more generally, an algebraically maximal Kaplansky field, we give an intrinsic construction of such a family which does not rely on a given truncation closed embedding. We also show that towers of complements and truncation closed embeddings can be extended from an arbitrary field to at least one of its maximal immediate extensions.</dcterms:abstract>
    <dc:language>eng</dc:language>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dc:contributor>Kuhlmann, Salma</dc:contributor>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-07-15T08:51:12Z</dc:date>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:creator>Fornasiero, Antongiulio</dc:creator>
  </rdf:Description>
</rdf:RDF>
Internal note
xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter
Contact
URL of original publication
Test date of URL
Examination date of dissertation
Method of financing
Comment on publication
Alliance license
Corresponding Authors der Uni Konstanz vorhanden
International Co-Authors
Bibliography of Konstanz
Yes
Refereed