Absorbing element

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In mathematics, an absorbing element for a binary relation * on a set S is an element a such that for all s in S, a*s=s*a=a. 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.^[1]