<Chapter Label =
"Ideals">
<Heading>
Ideals
</Heading>
In this chapter we describe the various ways that an ideal of a semigroup
can be created and manipulated in &SEMIGROUPS;.
<P/>
We write <E>ideal</E> to mean two-sided ideal everywhere in this chapter.
<P/>
The methods in the &SEMIGROUPS; package apply to any ideal of a semigroup
that is created using the function <Ref Func =
"SemigroupIdeal"/> or
<C>SemigroupIdealByGenerators</C>. Anything that can be calculated for a
semigroup defined by a generating set can also be found for an ideal. This
works particularly well for regular ideals, since such an ideal can be
represented using a similar data structure to that used to represent a
semigroup defined by a generating set but without the necessity to find a
generating set for the ideal. Many methods for non-regular ideals rely on
first finding a generating set for the ideal, which can be costly (but not
nearly as costly as an exhaustive
enumeration of the elements of the ideal).
We plan to improve the functionality of &SEMIGROUPS; for non-regular ideals
in the future.
<Section Label =
"Creating ideals">
<Heading>
Creating ideals
</Heading>
<#
Include Label =
"SemigroupIdeal">
<#
Include Label =
"Ideals">
</Section>
<Section Label =
"Attributes of ideals">
<Heading>
Attributes of ideals
</Heading>
<#
Include Label =
"GeneratorsOfSemigroupIdeal">
<#
Include Label =
"MinimalIdealGeneratingSet">
<#
Include Label =
"SupersemigroupOfIdeal">
</Section>
</Chapter>
