无单位元的群分次环、Smash积及其一个应用

Graded Rings Without Identity、Smash Product and An Application

中文关键词:  群分次环  Smash积  分次右完全环．

英文关键词:group-graded ring  Smash praduct  graded right perfect ring.

中文摘要:

      本文对于具有局部单位元的群分次环Ｒ证明了左Ｒ＃Ｃ^*－模范畴与分次左Ｒ－模范畴是同构的，并给出Ｒ是分次右完全环的一些充要条件．

英文摘要:

      For any group G and G-graded ring R with local units, we prove that the categories of unital graded R-modules and unital R#G^*-modules are isomorphic. Furthermore the categories isomorphism is applied to obtain some results of the graded perfect rings.