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

Wei, Junchao

Southeast Asian Bull. Math. 31, No. 5, 1009-1018 (2007).

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

Keywords:

von Neumann regular rings; YJ-injective modules; strongly right min-Abel rings; strongly regular rings