摘要
在一般Monoid—分次环 (未必有 1)范畴中 ,给出了分次Bear根 ,分次Koethe根 ,分次Levitizki根和分次Brown -McCoy -根的元素特性 ,并分别给出了对应于这几个根的分次半单环的结构定理 ,指出了分次环A = x∈MAx 的分次根和结合环Ae 的根之间的密切关系。
In this note ,we characterize the graded Bear radical,graded koethe radical,graded Levitizki radical and graded Brown-McCoy radical in the category of associative monoid-graded rings (not necessarily with 1) and grade-preserving ring homomorphisms,with element properties.Meawhile,we give the structure theorems of graded Semisimple graded rings corresponding these graded radicals and show the radical of A and A e are related closely.
