摘要
该文讨论了左FP-内射环和左IF环,证明了没有非零幂零元的左FP-内射环是Von Neumann正则环。以及给出了左IF环的一个特征性质:环R是左IF环当且仅当R是右H-凝聚环且任意有限表示左R-模是自反的。所得结果推广了S.Jain和E.Matlis的相应结果。
This paper discussed left FP-injective rings and left IF rings. Itproved that a left FP-injective ring without nonzero nilpotent elements is aVon Neumann regular ring and presents a characteristic property of left IFring, namely,a ring,is a left IF ring if and only if it is right H-coherent andall finite present left R -modules are reflex. These results extend the results ofS. Jain and E. Matlis.
关键词
结合环
模
同调代数
FP-内射环
associative ring
module (mathematics)
homological algebra
injective
exact
IF ring
Von Neumann regular ring
