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Semiprimitivity of Group Rings

In: Classically Semisimple Rings

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  • Martin Mathieu

    (Queen’s University Belfast, School of Mathematics and Physics)

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.

Suggested Citation

  • Martin Mathieu, 2022. "Semiprimitivity of Group Rings," Springer Books, in: Classically Semisimple Rings, chapter 10, pages 131-143, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-14209-3_10
    DOI: 10.1007/978-3-031-14209-3_10
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