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Semisimple 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 classical theory of semisimple algebras is one of the most striking examples how “module theoretical” methods produce deep structural results. Moreover, semisimple algebras and their representations play a very important role in many parts of mathematics. In this chapter, we establish the most fundamental properties of semisimple algebras and their modules, and prove the Wedderburn-Artin theorem which gives complete classification of such algebras. The results of Chapter 1 (in particular, of Sect. 1.7) and a description of the homomorphisms of simple modules, the so-called Schur’s lemma, will play a fundamental role in this process.

Suggested Citation

  • Yurij A. Drozd & Vladimir V. Kirichenko, 1994. "Semisimple Algebras," Springer Books, in: Finite Dimensional Algebras, chapter 2, pages 31-43, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-76244-4_2
    DOI: 10.1007/978-3-642-76244-4_2
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