Semissimplicidade de anéis de grupos e o teorema de Perlis-Walker

Abstract

Given a ring R and a group G, consider the group ring RG. In thiswork, based on [5], we presente a proof of Maschke's theorem obtained by Heinrich Maschke. This theorem gives necessary and sufficient conditions for the group ring RG to be semisimple. As a consequence, we present the main result of our study, the Perlis-Walker Theorem, which characterizes the simple components of KG, the group algebra of a finite abelian group G over a field K, when char(...)