# Absorbing element

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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:
Zero element. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Zero_element&oldid=39300