# Monoid

algebraic structure with an associative operation and a neutral elementary

In abstract algebra, a monoid is a set of elements with two key properties

1. It can be combined associatively; e.g. ${\displaystyle (A+B)+C=A+(B+C)}$
2. There exists an identity element; e.g. ${\displaystyle 1\times X=X}$, or ${\displaystyle 0+X=X}$

In computing science common monoids include addition, multiplication, or, and. These properties are useful for various problems e.g. they allow a large set of data to be divided, processed in parallel and combined. As each part produces a Monoid, the final combined result will be the same. This also works with more complex Monoids e.g. a map of word counts.