分次根、弱分次根与自反根  

The Graded Radicals, Weakly Graded Radicals and Reflected Radicals

作　　者：王尧[1] 任艳丽[1] 

机构地区：[1]鞍山师范学院数学系,鞍山114005

出　　处：《数学学报（中文版）》1999年第1期71-76,共6页Acta Mathematica Sinica：Chinese Series

基　　金：辽宁省教委科研基金

摘　　要：本文在一般群分次环范畴中，给出了典型分次根NG，LG，gG，rG和KG的元素刻划.通过建立弱分次根概念，研究了自反根Nref，Lref，gref，rref和Kref的性质，探讨了这些分次根和与它们相对应的自反根的关系．In the category of general group-graded rings and graded-preserving ring homomorphisms, the characterizations of classical graded radical NG, LG, gG, rG and KG by means of elements are presented, the constructions of Nref, Lref, gref, rref and Kref are investigated and the relations between these graded radicals and their corresponding reflected radicals are discussed by introducing the weakly graded radicals.

关 键 词：分次环 分次根 弱分次根 自反根 群分次环 

分 类 号：O153.3[理学—数学]