Certain Rings Whose Simple Singular Modules Are nil-injective

In this paper, we first study some characterizations of left min-abel ring, strongly left min-abel ring and left MC2 ring. Next, we discuss and generalize some well known results for a ring whose simple singular left modules are nil- injective. Finally, as a byproduct of these results we are able to show that if R is a left GMC2 left Goldie ring whose every simple singular left R− module is Y J− injective, then R is a finite product of simple left Goldie ring.