Number ring should be a special case of applying the concept of ring to numbers. The elements of a ring can be numbers or other abstract elements, such as functions that meet the definition of a ring.

ring

An algebraic system with two binary operations. 19th century, when abstract algebra came into being, mathematicians began to study sets satisfying all the laws of synthesis (i.e. additive commutative law, associative law, multiplicative commutative law, associative law, distributive law of multiplication to addition, etc.). ) or some of them. If a set has the properties of addition, multiplication and corresponding operations, it is called a ring. The integer set z forms a (number) ring.

Digital ring

Digital ring

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, the integer set z is a number ring.

Properties of number rings

Property 1 Any number ring contains zero (that is, the 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.