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On SF-rings and Regular Rings
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  • Journal title : Kyungpook mathematical journal
  • Volume 53, Issue 3,  2013, pp.397-406
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2013.53.3.397
 Title & Authors
On SF-rings and Regular Rings
Subedi, Tikaram; Buhphang, Ardeline Mary;
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A ring R is called a left (right) SF-ring if simple left (right) R-modules are flat. It is still unknown whether a left (right) SF-ring is von Neumann regular. In this paper, we give some conditions for a left (right) SF-ring to be (a) von Neumann regular; (b) strongly regular; (c) division ring. It is proved that: (1) a right SF-ring R is regular if maximal essential right (left) ideals of R are weakly left (right) ideals of R (this result gives an affirmative answer to the question raised by Zhang in 1994); (2) a left SF-ring R is strongly regular if every non-zero left (right) ideal of R contains a non-zero left (right) ideal of R which is a W-ideal; (3) if R is a left SF-ring such that is an essential left (right) ideal for every right (left) zero divisor x of R, then R is a division ring.
Left SF-rings;von Neumann regular rings;strongly regular rings;weakly left ideals;W-ideals;
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