<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --> <!-- %% --> <!-- %A semigrp.xml GAP documentation Thomas Breuer --> <!-- %% --> <!-- %% --> <!-- %Y (C) 1998 School Math and Comp. Sci., University of St Andrews, Scotland --> <!-- %Y Copyright (C) 2002 The GAP Group --> <!-- %% -->
<Chapter Label="Semigroups">
<Heading>Semigroups and Monoids</Heading>
This chapter describes functions for creating semigroups and monoids
and determining information about them.
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Properties of Semigroups">
<Heading>Properties of Semigroups</Heading>
The following functions determine information
about semigroups.
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Ideals of semigroups">
<Heading>Ideals of semigroups</Heading>
Ideals of semigroups are the same as ideals of the semigroup when
considered as a magma.
For documentation on ideals for magmas, see <Ref Func="Magma"/>.
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Congruences on semigroups">
<Heading>Congruences on semigroups</Heading>
An equivalence or a congruence on a semigroup is the
equivalence or congruence on the semigroup considered as a magma.
So, to deal with equivalences and congruences on semigroups,
magma functions are used.
For documentation on equivalences and congruences on magmas,
see <Ref Func="Magma"/>.
Given a semigroup and a congruence on the semigroup, one
can construct a new semigroup: the quotient semigroup.
The following functions deal with quotient semigroups in &GAP;.
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