A unital ring is an integral domain (or simply domain) if it has no zero divisors (i.e. implies either or ). For example, the ring of integers, any skewfield, the ring of global sections of the structure sheaf of any integral scheme, an Ore extension of any other integral domain.
In constructive mathematics, one wants to phrase the condition as whenever and , where is a tight apartness relation relative to which the ring operations are strongly extensional. (Of course, if the underlying set of the ring has decidable equality —as is true of , , , finite fields, etc— then none of this matters.)