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Central Simple Algebras

In: Finite Dimensional Algebras

Author

Listed:
  • Yurij A. Drozd

    (Kiev Taras Shevchenko University, Faculty of Mechanics and Mathematics)

  • Vladimir V. Kirichenko

    (Kiev Taras Shevchenko University, Faculty of Mechanics and Mathematics)

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.

Suggested Citation

  • Yurij A. Drozd & Vladimir V. Kirichenko, 1994. "Central Simple Algebras," Springer Books, in: Finite Dimensional Algebras, chapter 4, pages 69-81, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-76244-4_4
    DOI: 10.1007/978-3-642-76244-4_4
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