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 : a ∗ z = z ∗ a = z
Equivalence.  No proof.
References.