In mathematics, and specifically in abstract algebra, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero. Integral domains are generalizations of the ring of integers and provide a natural setting for studying divisibility. In an integral domain the cancellation property holds for multiplication by a nonzero element a, that is, if a ≠ 0, an equality ab = ac implies b = c.