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- Title
On SF-rings and Regular Rings.
- Authors
SUBEDI, TIKARAM; BUHPHANG, ARDELINE MARY
- Abstract
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) yon 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 l(χ) (r(χ)) is an essential left (right) ideal for every right (left) zero divisor χ of R, then R is a division ring.
- Subjects
RING theory; MATHEMATICAL regularization; MODULES (Algebra); MATHEMATICAL proofs; VON Neumann regular rings; DIVISION rings; IDEALS (Algebra)
- Publication
Kyungpook Mathematical Journal, 2013, Vol 53, Issue 3, p397
- ISSN
1225-6951
- Publication type
Article
- DOI
10.5666/KMJ.2013.53.3.397