The Rings of Integers refer to the set of whole numbers, including positive numbers, negative numbers, and zero. This set is denoted by the symbol ℤ, which comes from the German word "Zahlen," meaning "numbers." In this mathematical structure, addition and multiplication are defined, allowing for various operations to be performed on the integers. A ring is a specific type of algebraic structure that satisfies certain properties, such as closure under addition and multiplication, the existence of an additive identity (zero), and the ability to add and multiply integers in a way that is associative and commutative. The Rings of Integers are fundamental in number theory and provide a foundation for more complex mathematical concepts.