In mathematics, an absorbing element (or annihilating element) is a special type of element of a set with respect to a binary operation on that set.
In semigroup theory, the absorbing element is called a zero element[1][2] because there is no risk of confusion with other notions of zero, with the notable exception: under additive notation zero may, quite naturally, denote the neutral element of a monoid.
Formally, let (S, •) be a set S with a closed binary operation • on it (known as a magma).
[2] 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.