An integral domain is a type of mathematical structure known as a ring, which is a set equipped with two operations: addition and multiplication. 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 also be zero. This property ensures that the multiplication behaves nicely, similar to the integers. Additionally, an integral domain must have a multiplicative identity, usually denoted as 1, and it must be commutative, meaning that the order of multiplication does not affect the result. Examples of integral domains include the set of integers, ℤ, and the set of polynomials with coefficients in a field, such as ℝ[x].