\(2\)-Galois groups and the Kaplansky radical

• Datum: 2018
• Hauptverfasser: Dario, Ronie Peterson, Engler, Antonio Jose
• Format: Artikel
• Sprache: English
• Veröffentlicht: Lugansk National Taras Shevchenko University 2018
• Schlagworte: Brauer group; free pro-\(2\) product; Galois group; \(2\)-henselian valuation ring; quadratic form; 12J10; 12F10
• Online Zugang: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/649
• Назва журналу: Algebra and Discrete Mathematics

An accurate description of the Galois group \(G_{F}(2)\) 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 \({G_{F}{(2)}}\) decomposes as a fre...