The Artin–Wedderburn Theorem

Martin Mathieu
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Martin Mathieu: Queen’s University Belfast, School of Mathematics and Physics

Chapter 7 in Classically Semisimple Rings, 2022, pp 73-92 from Springer

Abstract: Abstract In this chapter, we shall obtain the full structure theorem for semisimple rings. This result, due to J. H. M. Wedderburn (1907) for semisimple finite-dimensional algebras and to E. Artin (1927) in the general case, enables us to determine completely this class of rings from the more elementary class of division rings. It is generally regarded as the first major result in the abstract structure theory of rings. In Sect. 7.2 below, we will briefly discuss the semisimplicity of group rings via Maschke’s Theorem 7.2.1. A detailed proof of the Hopkins–Levitzki theorem, already stated in 5.3.2 , is given in Sect. 7.3.

Date: 2022
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DOI: 10.1007/978-3-031-14209-3_7

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