Monoid

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

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

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.

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