monoid
Sign in to saveIn abstract algebra, a monoid is a set equipped with an associative binary operation and an identity element. For example, the natural numbers with addition form a monoid, the identity element being .
Article
24 sectionsContents
- Definition
- Monoid structures
- Submonoids
- Generators
- Commutative monoid
- Partially commutative monoid
- Examples
- Properties
- Products and powers
- Invertible elements
- Grothendieck group
- Types of monoids
- Acts and operator monoids
- Monoid homomorphisms
- Equational presentation
- Relation to category theory
- Monoids in computer science
- MapReduce
- Complete monoids
- See also
- Notes
- Citations
- References
- External links
In abstract algebra, a monoid is a set equipped with an associative binary operation and an identity element. For example, the natural numbers with addition form a monoid, the identity element being .
Monoids are semigroups with identity. Such algebraic structures occur in several branches of mathematics.