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
Famous quotes containing the word property:
“When a strong man, fully armed, guards his castle, his property is safe. But when one stronger than he attacks him and overpowers him, he takes away his armor in which he trusted and divides his plunder.”
—Bible: New Testament, Luke 11:21.22.