for a binary operation $*$ on a set $A$
An element $z$ is (left) absorbing if for all $a \in A$ we have $z * a = z$. Right absorbing elements are defined analogously. A two-sided absorbing element is both left and right absorbing: $z*a = a*z = z$ for all $a$. A two-sided absorbing element is unique.
See also Zero.
Absorbing element. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Absorbing_element&oldid=35961