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Zero Product Property


The zero product property asserts that, for elements a and b,

 ab=0=>a=0 or b=0.

This property is especially relevant when considering algebraic structures because, e.g., integral domains are rings having the zero product property and are important objects of study because of that fact.


See also

Integral Domain, Ring, Zero Divisor

This entry contributed by Christopher Stover

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Cite this as:

Stover, Christopher. "Zero Product Property." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ZeroProductProperty.html

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