ON FILTERS OF IMPLICATIVE n.p.o. SEMIGROUPS

Abstract

The concepts of implicative filters and derivations are introduced in implicative n.p.o. semigroups and studied their properties in connection with each other. The relation between order filters and implicative filters is also studied. The notion of implicative congruences is introduced in implicative n.p.o. semigroups. Finally, the equivalency between the existences of idempotent derivations and implicative filters is obtained.