Semiprime SF-rings whose essential left ideals are two-sided

Abstract

It is proved that if R is a semiprime ELT-ring and every simple right R-module is flat then R is regular. Is R regular if R is a semiprime ELT-ring and every simple right R-module is flat? In this note, we give a positive answer to the question.

Keywords

• (Von Neumann) regular ring
• SF-ring
• ELT-ring.