Generalized Principally Injective Maximal Ideals

We investigate in this paper von Neumann regularity of rings whose maximal right ideals are GP-injective. Actually, it is proved that a ring R is strongly regular if and only if R is a 2-primal ring whose maximal right ideals are GP-injective. It is also proved that if R is a PI-ring whose maximal right ideals are GP-injective, then R is strongly π-regular.