Definition
Formally, let (S, ∘) be a set S with a binary operation ∘ on it (known as a magma). A zero element is an element z such that for all s in S, z∘s=s∘z=z. A refinement are the notions of left zero, where one requires only that z∘s=z, and right zero, where s∘z=z.
Absorbing elements are particularly interesting for semigroups, especially the multiplicative semigroup of a semiring. In the case of a semiring with 0, the definition of an absorbing element is sometimes relaxed so that it is not required to absorb 0; otherwise, 0 would be the only absorbing element.
Read more about this topic: Absorbing Element
Famous quotes containing the word definition:
“According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animals—just as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.”
—Ana Castillo (b. 1953)
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)