摘要
本文解决Szasz.F.A在中提出的问题63,得到定理,设R是结合环,则以下命题等价:①环R=M(R)(?)(M(R))②R的每个主理想(a)的Von Neumann正则根M((a))是(a)的直和项.③(a)=M((a))(?)(M((a)),Va∈R同时对环的Von Neumann正则根的性质做了进一步的讨论、并且我们将得到的结果相应地推到环的弱正则根上.
In this paper, We solued the open problem 63 that Szasz.F.A aris-ed in [1]. We abtained:
Theorem: Let R be a associative ring, then the following equivalent prop-erties hold,
(1)R = M(R)(M(R))* ,
(2)The Von Neumann regular radical M((a)) of every principal idea (a)of R is a direct submmand of (a).
(3)(a)=M((a))(M((a)))* for every a of R.
We deeply discuss the properties of Von Neumann regular radical of Ri-ngs. At the same time, We generalize our results to Weakly regular radical of Rings.
出处
《黑龙江大学自然科学学报》
CAS
1989年第4期80-83,共4页
Journal of Natural Science of Heilongjiang University
关键词
结合环
正则根
正则环
Von Neumann regular-radical, Weakly regular radical radical.
