| Von-Neumann Regularity of N-rings |
| Received:January 05, 1998 |
| Key Words:
regular rings N-rings SF-rings SF-rings p-V-rings.
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| Fund Project: |
| Author Name | Affiliation | | WU Jun | Dept. of Math., Nanjing University, Jiangsu 210093, China
Dept. of Math., Anhui Normal Uuiversity, Wuhu, 241000, China | | YIN Xiao-bin | Dept. of Math., Nanjing University, Jiangsu 210093, China
Dept. of Math., Anhui Normal Uuiversity, Wuhu, 241000, China |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2001.02.020 |
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