1.28 Monoid Records and Semigroup Records

Like other domains semigroups and monoids are represented by records. While it is possible to construct such a record by hand it is preferable to have the functions SemiGroup (see SemiGroup) or Monoid (see Monoid) do this for you.

After such a record is created one can add record components. But you may not alter the values of components which are already present.

A semigroup or monoid record has the following category components.


is always true since a monoid or a semigroup is a domain.


is always true for semigroups.


is always true for monoids. The following components are the identification components of a semigroup or monoid record.


is a list of generators of the monoid or the semigroup. Duplicates are allowed in this list, but in the case of a monoid none of the generators may be the identity.


is the indentity in the case of a monoid.

Other components which contain information about the semigroup or monoid may be present.


is the size of the monoid or the semigroup (see "Size").


is the set of elements of the monoid or the semigroup (see "Elements").

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Version 2.4 (May 1998)