noun

pronunciation:

[ˈintigrəl dōˈmān]

meaning:

is a nonzero commutative ring in which the product of any two nonzero elements is nonzero.

example:

The ring $\mathbb {Z} [x]$ of all polynomials in one variable with integer coefficients is an integral domain.

property:

In an integral domain, every nonzero element a has the cancellation property, that is, if a ≠ 0, an equality ab = ac implies b = c.