An integral domain is a type of mathematical structure known as a ring, which has specific properties. It is a set equipped with two operations, addition and multiplication, that satisfy certain rules. In an integral domain, there are no zero divisors, meaning that if the product of two elements is zero, at least one of those elements must be zero. Additionally, an integral domain must have a multiplicative identity, usually denoted as 1, and it must be commutative under multiplication. Common examples of integral domains include the set of integers, ℤ, and the set of polynomials with coefficients in a field, such as ℝ[x] or ℚ[x].