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.
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... we may allow the coefficients and to come from any integral domain.) By the zero-product property, it follows that either or ... By the zero-product property, it follows that are the only roots of any root of must be a root of for some ...
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