Abstract: In this paper,we define the left rank of a ring Rand discuss the relations between a left ore reng Rand its left classical quotient ring Q on the properties of their ideals and left ranks.Also we gave four equivalent types of the proposition:a ring Rhas a left classical quotient ring Qand Qis a division ring.As an application of this result,we gave a brief proof method which different from [2]on the theorem of the Goldie Prime rings.