monoid (original) (raw)
A monoid is a semigroup G which contains an identity element
; that is, there exists an element e∈G such that e⋅a=a⋅e=a for all a∈G.
If e and f are identity elements of a monoid G, then e=e⋅f=f⋅e=f, so we may speak of “the” identity element of G.
A monoid homomorphism from monoids G to H is a semigroup homomorphism f:G→H such that f(eG)=eH, where eG,eH are identity elements of G and H respectively.
| Title | monoid |
|---|---|
| Canonical name | Monoid |
| Date of creation | 2013-03-22 11:50:15 |
| Last modified on | 2013-03-22 11:50:15 |
| Owner | djao (24) |
| Last modified by | djao (24) |
| Numerical id | 9 |
| Author | djao (24) |
| Entry type | Definition |
| Classification | msc 20M99 |
| Classification | msc 34-01 |
| Synonym | homomorphism |
| Related topic | Semigroup |
| Defines | monoid homomorphism |