Group theory and generalizations Groupoids, semigroups and further generalizations Concept
Monoid
Summary
A monoid is a semigroup that has an identity element. Examples are the natural numbers with addition and the maps from a set to itself with composition.
Where this leads
19 pages build on this one.
- Free monoid
- Kleene algebra
- Dynamical system
- Monoid ring
- Topological monoid
- Eilenberg–Moore category
- Endomorphism monoid
- Algebra over a monad
- Transformation semigroup
- Monoid object
- Algebra over an operad
- Gordan's lemma
- Grothendieck group
- Product category
- Idempotent semiring
- Semiring
- MV-algebra
- Relation algebra
- Green's relations
Further reading
- Web https://en.wikipedia.org/wiki/Monoid, Definition
About this page
| Tag | 0N6R902FG1 |
|---|---|
| URI | m2://0N6R902FG1 |
| Kind | concept |
| Writing | W1 stated |
| MSC | 20M10 |
| Specializes | Semigroup |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Definitions
Used by
- Free monoid
- Dynamical system
- Monoid ring
- Topological monoid
- Eilenberg–Moore category
- Endomorphism monoid
- Algebra over a monad
- Transformation semigroup
- Monoid object
- Algebra over an operad
- Gordan's lemma
- Grothendieck group
- Product category
- Semiring
- MV-algebra
- Relation algebra
- Green's relations