2-Galois groups and the Kaplansky radical
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
2-Galois groups and the Kaplansky radical
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| Creator |
Dario, R.P.
Engler, A.J. |
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| 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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| Date |
2019-06-15T20:39:32Z
2019-06-15T20:39:32Z 2010 |
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| Type |
Article
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| Identifier |
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.. http://dspace.nbuv.gov.ua/handle/123456789/154763 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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