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.

isDomain:

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

isSemiGroup:

is always true for semigroups.

isMonoid:

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

generators:

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.

identity:

is the indentity in the case of a monoid.

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

size:

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

elements:

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

  
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