CLASSIFICATION OF RAMIFIED DISCRETELY VALUED HENSELIAN DIVISION ALGEBRAS WITH INVOLUTIONS
https://doi.org/10.29235/1561-8323-2018-62-2-135-139
Abstract
The aim of the paper is to classify ramified division algebras with unitary involutions over discretely valued Henselian fields in terms of their residual algebras and special generators.
About the Authors
V. I. Yanchevskii
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Academician, D. Sc. (Physics and Mathematics), Professor, Head of the Department
Belarus
Academician, D. Sc. (Physics and Mathematics), Professor, Head of the Department
A. A. Ryzhkov
Belarusian State University
Belarus
Undergraduate
Belarus
Undergraduate
References
1. Yanchevskii V. I., Ryzhkov A. A. Structure of ramified discretely valued Henselian division algebras with involutions. Doklady Natsional’noi akademii nauk Belarusi = Doklady of the National Academy of Sciences of Belarus, 2018, vol. 62, no. 1, pp. 7–12 (in Russian).
2. Tikhonov S. V., Yanhevskii V. I. Homomorphisms and Involutions of Unramified Henselian Division Algebras. Journal of Mathematical Sciences, 2015, vol. 209, no. 4, pp. 657–664. DOI: 10.1007/s10958-015-2519-x
3. Jančevskiĭ V. I. Reduced unitaryk-theory and division rings over discretely valued hensel fields. Mathematics of the USSR – Izvestiya, 1979, vol. 13, no. 1, pp. 175–213. DOI: 10.1070/IM1979v013n01ABEH002018
4. Tikhonov S. V., Yanchevskii V. I. Symmetric Elements, Hermitian Forms, and Cyclic Involutions. Communications in Algebra, 2015, vol. 43, no. 11, pp. 4735–4744. DOI: 10.1080/00927872.2014.952011
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