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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 .
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- Commons category
- Monoids
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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.
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natural number
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ring
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associativity
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semigroup
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category
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magma
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partially ordered set
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concurrent computing
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quasigroup
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monoid object
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Transformation semigroup
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computer science
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International Standard Book Number
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complex number
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integer
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linear algebra
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real number
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rational number
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computer programming
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set
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