2-Galois groups and the Kaplansky radical
An accurate description of the Galois group GF(2) of the maximal Galois 2-extension of a field F may be given for fields F admitting a 2-henselian valuation ring. In this note we generalize this result by characterizing the fields for which GF(2) decomposes as a free pro-2 product F∗H where F is a f...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2010 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2010
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/154763 |
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| Zitieren: | 2-Galois groups and the Kaplansky radical / R.P. Dario, A.J. Engler // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 2. — С. 29–50. — Бібліогр.: 19 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862661885006970880 |
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| author | Dario, R.P. Engler, A.J. |
| author_facet | Dario, R.P. Engler, A.J. |
| citation_txt | 2-Galois groups and the Kaplansky radical / R.P. Dario, A.J. Engler // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 2. — С. 29–50. — Бібліогр.: 19 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | An accurate description of the Galois group GF(2) of the maximal Galois 2-extension of a field F may be given for fields F admitting a 2-henselian valuation ring. In this note we generalize this result by characterizing the fields for which GF(2) decomposes as a free pro-2 product F∗H where F is a free closed subgroup of GF(2) and H is the Galois group of a 2-henselian extension of F. The free product decomposition of GF(2) is equivalent to the existence of a valuation ring compatible with the Kaplansky radical of F. Fields with Kaplansky radical fulfilling prescribed conditions are constructed, as an application.
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| first_indexed | 2025-12-02T12:57:03Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154763 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| language | English |
| last_indexed | 2025-12-02T12:57:03Z |
| publishDate | 2010 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Dario, R.P. Engler, A.J. 2019-06-15T20:39:32Z 2019-06-15T20:39:32Z 2010 2-Galois groups and the Kaplansky radical / R.P. Dario, A.J. Engler // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 2. — С. 29–50. — Бібліогр.: 19 назв. — англ. 2000 Mathematics Subject Classification:12J10; 12F10.. https://nasplib.isofts.kiev.ua/handle/123456789/154763 An accurate description of the Galois group GF(2) of the maximal Galois 2-extension of a field F may be given for fields F admitting a 2-henselian valuation ring. In this note we generalize this result by characterizing the fields for which GF(2) decomposes as a free pro-2 product F∗H where F is a free closed subgroup of GF(2) and H is the Galois group of a 2-henselian extension of F. The free product decomposition of GF(2) is equivalent to the existence of a valuation ring compatible with the Kaplansky radical of F. Fields with Kaplansky radical fulfilling prescribed conditions are constructed, as an application. This work is part of the Ph. D. dissertation of the first author at Campinas StateUniversity under the supervision of the second author. Financial support for this researchwas provided by CAPES. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics 2-Galois groups and the Kaplansky radical Article published earlier |
| spellingShingle | 2-Galois groups and the Kaplansky radical Dario, R.P. Engler, A.J. |
| title | 2-Galois groups and the Kaplansky radical |
| title_full | 2-Galois groups and the Kaplansky radical |
| title_fullStr | 2-Galois groups and the Kaplansky radical |
| title_full_unstemmed | 2-Galois groups and the Kaplansky radical |
| title_short | 2-Galois groups and the Kaplansky radical |
| title_sort | 2-galois groups and the kaplansky radical |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154763 |
| work_keys_str_mv | AT dariorp 2galoisgroupsandthekaplanskyradical AT engleraj 2galoisgroupsandthekaplanskyradical |