# Absorbing element

From Citizendium

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.