Separable 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 6 in Finite Dimensional Algebras, 1994, pp 104-116 from Springer

Abstract: Abstract Those algebras which remain semisimple under arbitrary ground field extensions play a particular role among the semisimple algebras. They are called separable. Examples of separable algebras are, on the one hand, central simple algebras, and on the other, separable fields. It turns out that a general case represents, in a certain sense, a combination of these two examples. Fur-thermore, we shall establish the following fundamental properties of separable algebras: semisimplicity of all bimodules, the Wedderburn-Malcev theorem on lifting separable quotient algebras (which will be used in Chapter 8 for a generalization of the “universal algebra” construction of Sect. 3.6) and non-degeneracy of the principal trace form (which plays an important role in the study of arithmetical properties of separable algebras).

Keywords: Characteristic Polynomial; Division Algebra; Simple Algebra; Invertible Element; Splitting Field (search for similar items in EconPapers)
Date: 1994
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DOI: 10.1007/978-3-642-76244-4_6

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