A Sufficient Condition of A Simple Ring to Be A Division Ring and the Classification of the Commutative Simple Ring

Using the properties of the ideal of the ring theory,we obtain a sufficient condition of a simple ring to be a division ring and its corollary,and with the weaker inverse proposition of Lagrange's theorem in the group theory,we get the conclusion that the group without proper subgroup must be a finite group of prime order.Furthermore,based on the results,we get a classification of the commutative simple ring,that is the commutative simple ring either a field or a zero multiplication ring with the prime base number.