ON SEMILLATICE-ORDERED SEMIGROUPS. A CONSTRUCTIVE POINT OF VIEW
DANIEL A. ROMANO Faculty of Mechanical Engineering, 78000 Banja Luka, 71, Vojvoda Stepa Stepanovic Street, Bosnia and Herzegovina, Faculty of Education, 76300 Bijeljina, Semberskih Ratara Street, Bosnia and Herzegovina, e-mail: bato49@hotmail.com
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 ΞT on factor-semigroup S/(E(I),Q(K)). Some basic properties of such constructed semigroups are given.
