Semiprimitivity of Group Rings

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

Chapter 10 in Classically Semisimple Rings, 2022, pp 131-143 from Springer

Abstract: Abstract The starting point for this chapter is the discussion around Maschke’s theorem, Theorem 7.2.1 , which provides us with conditions under which the group ring K[G] is semisimple, provided G is a finite group. For any field K, the elements of G form a basis of the K-vector space K[G] and if the ring K[G] is semisimple, then it is necessarily Artinian, hence finite dimensional (Corollary 6.2.5 and Exercise 5.6 ). As a result, we cannot expect K[G] to be semisimple for an infinite group G.

Date: 2022
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DOI: 10.1007/978-3-031-14209-3_10

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