N-环Von-Neumann正则性

Von-Neumann Regularity of N-rings

中文关键词:  正则环  N-环  SF-环  p-V-环.

英文关键词:regular rings  N-rings  SF-rings  SF-rings  p-V-rings.

中文摘要:

      环R称为N-环，如果R的素根N(R)=｛r∈R｜存在自然数n使rⁿ=0}.本文不仅对N-环进行了刻划，而且还研究了N-环的VonNeumann正则性.特别证明了：对于N-环R，如下条件是等价的：(1)R是强正则环；(2)R是正则环；(3)R是左SP-环；(4)R是右SF-环；(5)R是MELT，左p-V-环；(6)R是MERT，右p-V-环.因此推广了文献[4]中几乎所有的重要结果，同时也改进或推广了其它某些有关正则环的有用结果.

英文摘要:

      A ring R is called a N-ring if N(R)==(r∈R｜ there is a natural number n such that rⁿ=0｝. In this paper, some new characterization of N-rings are given. Furthermore, the Von Neumann regularity of N-rings is also considered. Particularly, we show the following result: for a N-ring R, the following conditions are equivalent: (1) R is a strongly regular ring; (2) R is a regular ring; (3) R is a left SF-ging; (4) R is right SF-ring; (5) R is a MELT, leftp-V-ring; (6) R is a MERT, right p-V-ring.