Abstract
Semilattice-ordered semigroup is an important algebraic structure. It is ordered semigroup under anti-order. Some basic properties of semillatice-ordered semigroups with apartness are given by constructive point of view. Let I and K be compatible, an ideal and an anti-ideal of semilattice-ordered semigroup S. Constructions of compatible congruence E(I) and anti-congruence Q(K) on S, generated by I and K respec-tively, are given. Besides, we construct compatible order and anti-order θT on factor-semigroup S/(E(I),Q(K)). Some basic properties of such constructed semigroups are given.
Cuvinte cheie
Constructive mathematics
semigroup with apartness
semilattice-ordered semigroup
order and antiorder relations
ideal and anti-ideal
congruence and anti-congruence