 For instance, if then , , , , , and so on; in general, "a""n" is going to be an integral linear combination of 1, "a", and "a"2.The first axiomatic definition of a ring was given by Adolf Fraenkel in 1914, but his axioms were stricter than those in the modern definition.For instance, he required every non-zero-divisor to have a multiplicative inverse.