LEFT $SF$-RINGS WHOSE COMPLEMENT LEFT IDEALS ARE IDEALS
XHANG JULE, DU XIANNENG
A ring $R$ is called a left (right) $SF$-ring if every simple left (right) $R$-module is flat. It is known that von Neumann regular rings are left and right $SF$-rings. In this note, we prove that if $R$ is a left $SF$-ring whose complement left ideals are ideals, then $R$ is strongly regular.