Zero Product Property
Definition
The zero product property (sometimes called the null factor law in the context of integers), is a property of certain rings that:
\[ ab = 0 \implies a = 0 \ \text{or} \ b = 0.\]
That is, there does not exist any non-zero zero divisors (examples).
A ring which has the zero product property is called a domain (ring theory) or an integral domain in the commutative case.