semigroup (original) (raw)
A semigroup G is a set together with a binary operation
⋅:G×G⟶G which satisfies the associative property: (a⋅b)⋅c=a⋅(b⋅c) for all a,b,c∈G.
The set G is not required to be nonempty.
Let G,H be two semigroups. A semigroup homomorphism from G to H is a function f:G→H such that f(ab)=f(a)f(b).
| Title | semigroup |
|---|---|
| Canonical name | Semigroup |
| Date of creation | 2013-03-22 11:50:08 |
| Last modified on | 2013-03-22 11:50:08 |
| Owner | djao (24) |
| Last modified by | djao (24) |
| Numerical id | 11 |
| Author | djao (24) |
| Entry type | Definition |
| Classification | msc 20M99 |
| Synonym | homomorphism |
| Related topic | groupoid |
| Related topic | Band2 |
| Related topic | SubmonoidSubsemigroup |
| Related topic | NullSemigroup |
| Related topic | ZeroElements |
| Related topic | Monoid |
| Defines | semigroup homomorphism |