关于分次环的分次性质和非分次性质

On Graded Properties and Non Graded Propertiesover Graded Rings

中文关键词:  左gr－自内射环  左gr－PF环  左gr－QF环  左gr-线性紧环

英文关键词:gr-PF  gr-QF  gr-linearly compact.

中文摘要:

      本文证明了对有限群分次环Ｒ而言，下列条件等价：（１）Ｒ是左ｇｒ－自内射环（左ｇｒ－ＰＦ环，左ｇｒ－ＱＦ环，左ｇｒ－线性紧环）．（２）Ｒ是左自内射环（左ＰＦ环，左ＱＦ环，左线性紧环）．（３）Ｒ＃Ｇ^*是左自内射环（左ＰＦ环，左ＱＦ环，左线性紧环）．

英文摘要:

      In this paper, we prove that a finite-group graded ring R is left gr-selfinjective,left gr-PF, left gr-QF and left gr-linearly compact if and only if R is left selfinjective, leftPF, left QF and left linearly compact if and only if its smash product R#G is left selfinjective, left PF, left QF and left linearly compact, repectively.