On YJ-Injective Modules and Characteristic Properties of Strongly Regular Rings

Let N(R)={x|x2=0,x∈R},write if l(a)(for any a∈N(R)) is a(two-sided) ideal of R.This paper studies the regularity of rings satisfy(*),and proved that if R satisfy(*) then following conditions are equivalent:(1) R is a strongly regular ring,(2) every maximal essential right ideal of R is YJ-injective,(3) R is a right GP-V-ring and every maximal essential right ideal of R is a generalized weakly ideal of R,(4) R is a left GP-V-ring and every maximal essential right ideal of R is a generalized weakly ideal of R.