Subfields of a real closed field of countable codimension
| dc.contributor.author | Gamboa Mutuberria, José Manuel | |
| dc.date.accessioned | 2023-06-17T08:28:49Z | |
| dc.date.available | 2023-06-17T08:28:49Z | |
| dc.date.issued | 2021-05-17 | |
| dc.description.abstract | Let R be a real closed field and let K be a subfield of R such that R/K is a proper algebraic extension. The main result of this paper (Theorem 2.6) states that there exists {Kn:n∈N} a countable family of countable codimension subfields of R containing K such that Ks⊆Kt if s∣t and R=⋃n∈NKn. Among other consequences of this result, it is shown that (Corollary 3.1) every real closed field contains a countable family of countable codimension subfields and (Proposition 3.7) if F is the family of all countable codimension subfields of a real closed field, then ⋂E∈FE=Q. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | FALSE | |
| dc.description.sponsorship | Ministerio de Economía y Competitividad (MINECO) | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/73990 | |
| dc.identifier.doi | 10.1016/j.jpaa.2021.106795 | |
| dc.identifier.issn | 0022-4049 | |
| dc.identifier.officialurl | https://doi.org/10.1016/j.jpaa.2021.106795 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/7244 | |
| dc.issue.number | 12 | |
| dc.journal.title | Journal of Pure and Applied Algebra | |
| dc.language.iso | eng | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | MTM2017-82105-P. | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 512 | |
| dc.subject.cdu | 512.623.3 | |
| dc.subject.keyword | Real closed field | |
| dc.subject.keyword | Galois theory | |
| dc.subject.keyword | Krull topology | |
| dc.subject.ucm | Álgebra | |
| dc.subject.unesco | 1201 Álgebra | |
| dc.title | Subfields of a real closed field of countable codimension | |
| dc.type | journal article | |
| dc.volume.number | 225 | |
| dcterms.references | [1] E. Artin, O. Schhreier: Algebraische Konstruction reeller Körper der reellen algebraische Zahlen. Hamb. Abh. 5, 85-99, (1926). [2] J. Bochnak, M. Coste, M.F. Roy: Real algebraic geometry. Translated from the 1987 French original. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 36. Springer-Verlag, Berlin, (1998). [3] J. Dieudonné: History of Algebraic Geometry. An Outline of the History and Development of Algebraic Geometry. Wadsworth Advanced Books, Monterey, CA. [4] J.M. Gamboa: Some new results on ordered fields. Journal of Algebra bf 110, 1-12, (1987). [5] J.M. Gamboa, T. Recio: Ordered fields with the dense orbits property. Journal of Pure and applied Algebra bf 30, 237-246, (1983). [6] N. Jacobson: Lectures in Abstract Algebra. III. Theory of fields and Galois Theory. Springer Verlag. 4. (1971). [7] H. Kestelman: Automorphisms of the ffield of complex numbers. Proc. London Math. Soc. (2), 53, 1-12, (1951). [8] S. Lang: Algebra. Addison-Wesley. Third printing. (1971). [9] D. Marker: Model theory. An introduction. Graduate Texts in Mathematics, 217 Springer-Verlag, New York. (2002). [10] P. J. Morandi: Field and Galois Theory. Graduate Texts in Mathematics, 167, Springer-Verlag, New York. (1996) [11] I. Shafarevich: Basic Algebraic Geometry. Springer-Verlag, Berlin. (1977) | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 8fcb811a-8d76-49a2-af34-85951d7f3fa5 | |
| relation.isAuthorOfPublication.latestForDiscovery | 8fcb811a-8d76-49a2-af34-85951d7f3fa5 |
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