Semigroup

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Demote once it has been fleshed out (to at least in line with monoid)

Note: not to be confused with monoids and groups. Note all groups are monoids and all monoids are semigroups.

Definition

A semigroup is a tuple, [ilmath](S,*)[/ilmath], consisting of a set, [ilmath]S[/ilmath] and a binary operation, [ilmath]*:S\times S\rightarrow S[/ilmath], where:

• [ilmath]*[/ilmath] is associative - [ilmath]\forall x,y,z\in S[(x*y)*z=x*(y*z)][/ilmath]