On Co-Ideals of Implicative Semigroups with Apartness

Abstract

The setting of this research is the Bishop’s constructive mathematics - a mathematics based on theIntuitionistic Logic and the principled-philosophical constructive orientation. Implicative semigroups with apartness were introduced and analyzed in 2016-17 in two published articles (An introduction to implicative semigroupswith apartness, Sarajevo J. Math., 12(25)(2)(2016), 155-165 and Strongly extensional homomorphism of implicative semigroups with apartness. Sarajevo J. Math., 13(2)(2017), 155-162). In this paper, as a continuation of thementioned articles, the concept of co-ideals was introduced in the implicative semigroups with apartness. Some ofthe important properties of these substructures in such semigroups have been proven. In addition, it has been shownthat the family of all co-ideals in these semigroups forms a complete lattice.