An Integer Ring is a mathematical structure that consists of the set of all integers, denoted as ℤ. This set includes positive numbers, negative numbers, and zero. In an integer ring, two operations are defined: addition and multiplication. These operations follow specific rules, such as associativity and distributivity, making the integer ring a fundamental concept in abstract algebra. In an integer ring, every integer can be added or multiplied with another integer, resulting in another integer. The integer ring also contains additive and multiplicative identities, which are 0 and 1, respectively. Additionally, every integer has an additive inverse, ensuring that the structure is closed under these operations.