## MONOID

### Monoid

In abstract algebra, a branch of mathematics, a**monoid**is an algebraic structure with a single associative binary operation and an identity element. Monoids are studied in semigroup theory as they are semigroups with identity. Monoids occur in several branches of mathematics; for instance, they can be regarded as categories with a single object. Thus, they capture the idea of function composition within a set. Monoids are also commonly used in computer science, both in its foundational aspects and in practical programming. The set of strings built from a given set of characters is a free monoid. The transition monoid and syntactic monoid are used in describing ...

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### monoid

#### Noun

- A set which is closed under an associative binary operation, and which contains an element which is an identity for the operation.

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