Semigroups

Magma supports the following categories of semigroups:

SgpFP

finitely presented semigroups

MonFP

finitely presented monoids

The generic free structures are created by the functions FreeSemigroup(n) and FreeMonoid(n), where n is the number of generators. One may create any semigroup by creating one of these structures and then forming the required quotient semigroup, using the syntax

       quo< SEMIGROUP | RELATIONS >

To abbreviate this process, these constructors apply:

       Semigroup< GENERATORS | RELATIONS >
       Monoid< GENERATORS | RELATIONS >

Example

> M<x, y>:=Monoid< x, y | x^2, y^2, (x*y)^2 >;
> print M;
Finitely presented monoid
Relations
    x^2 = Id(M)
    y^2 = Id(M)
    (x * y)^2 = Id(M)