Definition 1. Let $M$ be a magma and $a \in M$.
-
$a$ is a left-absorbing element if for all $x \in M$,
\[ax = a.\] -
$a$ is a right-absorbing element if for all $x \in M$,
\[xa = a.\] -
$a$ is an absorbing element if it is both left- and right-absorbing.