Let s be a nonempty subset of a complex set. If the sum, difference and product of any two numbers in S still belong to S, then S is called a number ring. For example, integer set Z is a number ring, rational number set Q, real number set R and complex number set C are all number rings. Let f be a number ring in the definition of number field. If a, b∈F and a≠0 are arbitrary, then b/a ∈ f; F is called the number field. For example, rational number set Q, real number set R and complex number set C are all number fields. Properties of number rings 1 Any number ring contains zero (that is, zero ring is the smallest number ring). Property 2 Let s be a number ring. If a∈S, then na∈S(n∈Z). Property 3 If both m and n are number rings, then M∩N is also number ring. The nature of number field Any number field contains rational number field Q. That is to say, q is the smallest number field. Number field: the result of sum, difference, product and quotient of any two numbers in a number set is still in the number set, then the number set is a number field; The number field contains 0, 1 and is closed. Generally speaking, there are three kinds: rational number field, real number field and complex number field. I hope my answer is helpful to you.