Definitions of a Field by Independent Postulates
Leonard Eugene Dickson · Transactions of the American Mathematical Society · 1903
Another definition is obtained by replacing 8 by the postulate : For any two elements a, b, such that e o a =f= c for at least one element c, there exists an element x such that (a a x) o b = b.In the proofs of independence given below, system S3 must now be modified.