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
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