## On simple singular YJ-injective modules.(English)Zbl 1141.16014

Summary: We investigate the strong regularity of rings whose simple singular right $$R$$-modules are YJ-injective. It is proved that the following conditions are equivalent for a ring $$R$$: (1) $$R$$ is strongly regular; (2) $$R$$ is a strongly right min-Abel right MERT ring and right weakly regular ring; (3) $$R$$ is a strongly right min-Abel right MERT ring whose simple singular right $$R$$-modules are YJ-injective; (4) $$R$$ is a wjc right quasi-duo ring whose simple singular right $$R$$-modules are YJ-injective. Several known results are unified and extended.

### MSC:

 16E50 von Neumann regular rings and generalizations (associative algebraic aspects) 16D50 Injective modules, self-injective associative rings 16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras