Definition 1.6.11.  Let X be a set, :X × X → X be an operation on X, z ∈ X. We define:
z is an absorbing element for   :⇔  z is a left absorbing element for  and z is a right absorbing element for   ⇔  ∀ a ∈ X : az = za = z
Equivalence.  No proof.
References.