Number rings are mathematical structures that consist of a set of numbers along with two operations: addition and multiplication. They follow specific rules, such as the ability to add and multiply any two numbers in the set and still remain within the set. This makes number rings a fundamental concept in abstract algebra, helping to understand more complex mathematical ideas. A common example of a number ring is the set of integers, denoted as ℤ. In this ring, you can add or multiply any two integers, and the result will always be another integer. Other examples include ℚ, the set of rational numbers, and ℝ, the set of real numbers, each with their own unique properties and applications.