A short proof by contradiction of this property consists of multiplying both sides of an equation by the multiplicative inverse of any factor on one side of the equation.
This property does not hold in the rings of integers modulo a composite number, and whether it holds distin- guishes integral domains with respect to rings. A short proof by contradiction of this property consists of multiplying both sides of an equation by the multiplicative inverse of any factor on one side of the equation. Often used to find so- lutions to polynomials of degree greater than one, this property makes the solutions obvious once the polynomial has been factored. Name this property that states that if quantities multiply to the additive identity then at least one of the quantities is equal to the additive identity—that is, zero.
This property does not hold in the rings of integers modulo a composite number, and whether it holds distin- guishes integral domains with respect to rings.
{zero} product property