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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]].

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How to Cite This Entry:
Absorbing element. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Absorbing_element&oldid=35961

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