Semisimple 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 2 in Finite Dimensional Algebras, 1994, pp 31-43 from Springer

Abstract: 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.

Date: 1994
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DOI: 10.1007/978-3-642-76244-4_2

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