2) graded socle
分次基座
1.
By using the properties of the socles,Jacobson radicals and graded Jacobson radicals of groupgraded modules,some concrete characterizations for graded socles of groupgraded rings and modules are obtained,and the relationship of socles,higherorder socles and graded socles of groupgraded rings are discussed.
利用群分次模的基座和Jacobson根、分次Jacobson根的性质,得到了群分次环与群分次模的分次基座的一些具体刻画,讨论了群分次环的基座、高阶基座和分次基座之间的关系。
2.
In this paper we devoted to study the socles and graded socles of group-graded rings and modules.
本文的主要目的是研究群分次环与群分次模的基座和分次基座,获得了有关环与模的Jacobson根的对偶的一些主要结果,推广了关于交叉积的一些相关结果。