In the branch of mathematics called algebra, the zero-product property states that the product of two nonzero elements is nonzero. In other words, it is the following assertion:
If, then either or .
The zero-product property is also known as the rule of zero product or nonexistence of zero divisors. All of the number systems studied in elementary mathematics — the integers, the rational numbers, the real numbers, and the complex numbers — satisfy the zero-product property. In general, a ring which satisfies the zero-product property is called a domain.
Read more about Zero-product Property: Algebraic Context, Examples, Non-examples, Application To Finding Roots of Polynomials
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—Samuel Johnson (1709–1784)