In the present paper, we have introduced some new definitions On M-cover ring, M-compact ring, weakly M-compact ring, weakly M-compact c. ring, M-compact c. ring, M-compact locally ring and M-compact strong locally ring, we obtain some examples and results related to M-cover ring, M-compact ring, weakly M-compact ring, weakly M-compact c. ring, M-compact c. ring, M-compact locally ring and M-compact strong locally ring. Keywords: rings, M-cover ring, M-compact ring, ring homomorphism, ring isomorphism
