# Absorbing element

From Encyclopedia of Mathematics

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*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.

**How to Cite This Entry:**

Absorbing element.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Absorbing_element&oldid=35961