Central Simple Algebras

Yurij A. Drozd and Vladimir V. Kirichenko
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Yurij A. Drozd: Kiev Taras Shevchenko University, Faculty of Mechanics and Mathematics
Vladimir V. Kirichenko: Kiev Taras Shevchenko University, Faculty of Mechanics and Mathematics

Chapter 4 in Finite Dimensional Algebras, 1994, pp 69-81 from Springer

Abstract: Abstract The Wedderburn-Artin theorem reduces the study of semisimple algebras to the description of division algebras over a field K. If D is a finite dimensional division algebra over K and C its center, then C is a field (an extension of the field K) and D can be considered as an algebra over the field C. In this way, the investigation is divided into two steps: the study of the extensions of the field K and the study of central division algebras, i. e. of division algebras whose center coincides with the ground field. It turns out that these are two separate problems. However, one can conveniently apply common methods of investigation based on the concept of a bimodule and tensor product of algebras.

Date: 1994
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DOI: 10.1007/978-3-642-76244-4_4

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