Absorbing element
From Citizendium, the Citizens' Compendium
In algebra, an absorbing element or a zero element for a binary operation has a property similar to that of multiplication by zero.
Formally, let 
be a binary operation on a set X. An element O of X is absorbing for if
holds for all x in X. An absorbing element, if it exists, is unique.
Examples
- The zero (additive identity element) of a ring is an absorbing element for the ring multiplication.
- The zero matrix is the absorbing element for matrix multiplication.
- The empty set is the absorbing element for intersection of sets.
