分次反单根及其分次补根

GRADED ANTISIMPLE RADICAL AND ITS GRADED SUPPLEMENTING.RADICAL

在群G是有限群时,构造了两个特殊类T,T′,使得K_G=T∪T′,其中K_G是全体有幂等分次心的分次亚直既约环的类;设α,α′分别表示由T,T′所确定的分次上根,则S_G=α∪α′,其中S_G是分次反单根;令R_G,R分别表示S_G,S的(分次)补根,则R_(ref)=R_G,而且R^G≤R_G。

For a finite group G, this paper makes two special classes T and T' such thatK_G=T∪T', where K_G for the class of all graded subdivectly irreducible rings with idempotent grinded hearts. Let α, α′ denote for the graded upper radicals determined by T and T' respectively, then S_G=α∩α′, where S_G for graded antisimple radicals Let R_G, R for the (graded) supplementing radicals of S_G and S respectively, then R_(ref)=R_G and R^G≤R_G.