Suppose is an algebraic structure. We might ask, does have the zero-product property? In order for this question to have meaning, must have both additive structure and multiplicative structure. Usually one assumes that is a ring, though it could be something else, e.g., the nonnegative integers .
Note that if satisfies the zero-product property, and if is a subset of, then also satisfies the zero product property: if and are elements of such that, then either or because and can also be considered as elements of .
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