Zero-product Property - Algebraic Context

Algebraic Context

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 .

Read more about this topic:  Zero-product Property

Famous quotes containing the words context and/or algebraic:

    Parents are led to believe that they must be consistent, that is, always respond to the same issue the same way. Consistency is good up to a point but your child also needs to understand context and subtlety . . . much of adult life is governed by context: what is appropriate in one setting is not appropriate in another; the way something is said may be more important than what is said. . . .
    Stanley I. Greenspan (20th century)

    I have no scheme about it,—no designs on men at all; and, if I had, my mode would be to tempt them with the fruit, and not with the manure. To what end do I lead a simple life at all, pray? That I may teach others to simplify their lives?—and so all our lives be simplified merely, like an algebraic formula? Or not, rather, that I may make use of the ground I have cleared, to live more worthily and profitably?
    Henry David Thoreau (1817–1862)