On von-Neumann Regular Rings and Left SF-Rings
Received:April 23, 2002  
Key Word: regular ring   strongly regular ring   SF-ring   generalized weak ideal.  
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Author NameAffiliation
ZHOU Hai-yan Dept. of Math.
Nanjing University
Jiangsu
China 
WANG Xiao-dong Dept. of Appl. Math. & Phys.
Anhui University of Science and Technology
Wuhu
China 
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Abstract:
      A rings R is defined to be a left SF-ring if all simple left R -modules are flat. It is known that von Neumann regular rings are SF-rings. But the question whether a left SF-ring is necessarily regular remains open. In this paper, we study the regularity of left SF-rings which satisfy certain additional conditions. It is proved that R is strongly regular if R is a left SF-ring whose maximal left (right) ideals are generalized weak ideals. Furthermore, we generalize some results in [3].
Citation:
DOI:10.3770/j.issn:1000-341X.2004.04.014
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