2-Galois groups and the Kaplansky radical

• Published in: Algebra and Discrete Mathematics
• Date: 2010
• Main Authors: Dario, R.P., Engler, A.J.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2010
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/154763
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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...