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періодичних видань НАН України
періодичних видань НАН України
2-Galois groups and the Kaplansky radical
Репозиторій DSpace/Manakin
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2-Galois groups and the Kaplansky radical
Інший ID:
2000 Mathematics Subject Classification:12J10; 12F10..
Посилання:
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.
Підтримка:
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.
Дата:
2010
Переглядів:
661
Завантажень:
206
Анотація:
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.
