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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Author NameAffiliation
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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