【摘要】 <正> 令R(G)表示环R上群G的群环,群环的根如何刻化,至今尚无很好的结果。对于群代数F(G)(F是域),[4],[5]已对个别群证明JF(G)可由G的某些子群控制,即JF(G)=JF(H)·F(G),(J—指Jacohson根)。H.K.Farahat进一步提出何时等式JR(G)=(JR)(G)成立。显然,这对刻化群环的根很有价值。它将R(G)的半单性转化为R的半单性。[6],[7]中当G是局部有限群。R分别是半准素环与交换环时,证明Farahat等式对J—根成立。[3]证明了当R是交换环,G是有限群时Farahat等式对BM—根成立。更多还原

【Abstract】 H. K. Farahat raised the problem that when is the equality JR(G)=(JR)(G) valid, where J denotes Jacobson radical. In this paper, we have solved that Farahat equality is true for Bear radical, Livitzki radical, Kothe radical, if R is Commutative ring with , G is any group. That is, (G)=(R)(G), R(G)=(R)(G), R(G)=(R)(G), respectively. Let G be group such that JF(G)=O, if Ch.F(G), where F is a Field. We obtained that JR(G)= (JR)(G), if R is an Artinian ring with 1, or R is an associative ring with 1, G is any group.更多还原