1) unit π-regular ring
幺π-正则环
1.
Moreover,we show that: If R is a left G-morphic ring,the same is true of eRe for every idempotent e∈R;Every unit π-regular ring is a left(right) G-morphic ring;Every left G-morphic ring is a right GP-injective ring.
我们给出了G-morphic环的定义,证明了如下主要结果:对R中的任意幂等元e,如果R是左G-morphic环,则eRe也是左G-morphic环;每一个幺π-正则环是左(右)G-morphic环;每一个左G-morphic环是右GP-内射环。
2) π-regular ring
π-正则环
1.
In this paper we study extensions of Abelian π-regular rings.
本文研究了Abelπ-正则环的扩张。
2.
Moreover,we show that: If R is a left G-morphic ring,the same is true of eRe for every idempotent e∈R;Every unit π-regular ring is a left(right) G-morphic ring;Every left G-morphic ring is a right GP-injective ring.
我们给出了G-morphic环的定义,证明了如下主要结果:对R中的任意幂等元e,如果R是左G-morphic环,则eRe也是左G-morphic环;每一个幺π-正则环是左(右)G-morphic环;每一个左G-morphic环是右GP-内射环。
3.
Some connections between AGP-injective rings and π-regular rings are given here.
给出了AGP-内射环与π-正则环的一些联系,证明了若R为reduced环,则R是左AGP-内射环当且仅当R是π-正则环,并着重讨论了满足一定条件的AGP-内射环是π-正则环。
3) π~*-regular ring
π~*-正则环
4) regular with an identity
含幺正则环
5) Abelian π-regular ring
Abel π-正则环
6) strongly π-regular rings
强π-正则环
1.
We also study the relationship among the Strongly regular rings,Strongly π-regular rings and Strongly Quasi-Clean rings.
本文定义强拟-C lean环,使用通常环论方法证明强拟-C lean环的同态象、直积、对角矩阵仍是强拟-C lean环,讨论强正则环、强π-正则环与强拟-C lean环之间的关系。
补充资料：小幺
1.旧称官府中供奔走的小差役。 2.旧称年轻娼妓。 3.少年男仆。
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