Semiprime SF-rings whose essential left ideals are two-sided. (English) Zbl 0814.16007

An associative ring \(R\) with identity is called ELT (MELT) if each essential (maximal) left ideal of \(R\) is two-sided. As a generalization of (von Neumann) regular rings, V. S. Ramamurthi [Proc. Am. Math. Soc. 48, 21-25 (1975; Zbl 0302.16024)] called \(R\) a right SF-ring if each simple right \(R\)-module is flat. It is an open question whether or not a right (or even two-sided) SF-ring is regular. In this paper, the authors prove that a semiprime ELT right SF-ring is regular. Recently, Y. Xiao [Can. Math. Bull. 37, 272-277 (1994; Zbl 0815.16003)] has improved this and shown that each MELT right SF-ring is regular.


16E50 von Neumann regular rings and generalizations (associative algebraic aspects)
16N60 Prime and semiprime associative rings
16D25 Ideals in associative algebras
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