An integer ring is a mathematical structure that consists of the set of all integers, including positive numbers, negative numbers, and zero. This set is denoted by the symbol ℤ. In an integer ring, you can perform addition, subtraction, and multiplication, and the results will always be another integer. One important property of integer rings is that they are closed under these operations, meaning that combining any two integers using these operations will yield another integer. Additionally, integer rings have an identity element for addition (0) and multiplication (1), making them a fundamental concept in abstract algebra.