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.
。整环是整数环的抽象化，它很好地继承了整数环的整除性质，使得我们能够更好地研究整除理论。