This note contains the following results: (1) A is strongly regular iff every non-zero factor ring of A is a semi-prime ring containing a non-zero reduced p-injective left ideal which is a left annihilator; (2) A is an ELT von Neumann regular ring iff A is a semi-prime MELT ring whose essential right ideals are idempotent iff A is a semi-prime ELT ring such that for any essential left ideal L of A, either AA/L is p-injective or A/LA is flat; (3) If A is a semi-prime ring whose simple left modules are either YJ-injective or projective, then the Jacobson radical of A is zero. If, further, each maximal right ideal of A is either injective or a two-sided ideal of A, then A is either strongly regular or right self-injective regular. Several conditions are given for a left Noetherian ring to be left Artinian.