1) 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。
2) π~*-regular ring
π~*-正则环
3) Abelian π-regular ring
Abel π-正则环
4) 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。
5) Semi-π-regular ring
半π-正则环
6) 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。
补充资料：正则环
正则环
*-regular ring
‘正则环卜一佣.山r对l招;一pe口朋钾Oe劝则。J 带有对合反自同构俐~“*的正则环(仰Nh助-姗愈义下的)(比州肚nllg(谊the别级侣e ofvon卜犯u-~”，使得戊扩=0蕴涵“二0二正则环的幂等元。称为一个投影算子(p咧戊tor)，若。*二。.，正则环的每个左(右)理想由唯一的投影算子生成.这样可以谈到·正则环的投影算子的格.若格是完全的，则是一个连续几何(contjnuous罗。能好).一个有齐次基“t，…，a。(。)4)的有补模格(m团过肚妞-石ce)(亦见有补格(】atti优俪伍comPlemet出))是有正交补的格，当且仅当它同构于某个，正则环的投影算子的格.
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条