From Maths
Jump to: navigation, search
Stub grade: A
This page is a stub
This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:
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.


A semigroup[1] 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]


  1. Abstract Algebra - Pierre Antoine Grillet

Template:Semigroup theory navbox