On the Radical of Group Rings |
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abelian group algebraically closed field artinian Brauer and Nesbitt Chosun University coefficient ring commutative ring completes the proof Corollary dim N(KG divides the order element of G field of ch field whose characteristic finite subgroup finitely generated abelian finitely generated subgroup following theorem forms a basis G is locally group G group of order group ring KG h₁ Hence ideal of KG implies infinite cyclic group integers irreducible isomorphic J(KG J(KH K-basis K-module Ker.f KG is semi-prime KG is semi-simple kn(G ko(G Lemma Let G Let H locally finite groups m-system maximal ideal modular representation theory nil ideals nilpotent elements nilpotent ideal normal p-Sylow subgroup normal subgroup p-element po(G prime ideal prime radical principal indecomposable module Proposition 1-1 prove the following radical of KG regular set of orders subdirect product subgroup H subgroup of G submodule subring Supp(x Suppose Theorem 1-3 totally ordered groups u₁