On Co-Ideals of Implicative Semigroups with Apartness

Authors : Daniel A ROMANO

Pages : 101-106

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Publication Date : 2019-12-31

Article Type : Research Paper

Abstract :The setting of this research is the Bishop`s constructive mathematics - a mathematics based on the Intuitionistic Logic and the principled-philosophical constructive orientation. Implicative semigroups with apartness were introduced and analyzed in 2016-17 in two published articles insert ignore into journalissuearticles values(\emph{An introduction to implicative semigroups with apartness}, Sarajevo J. Math., 12insert ignore into journalissuearticles values(25);insert ignore into journalissuearticles values(2);insert ignore into journalissuearticles values(2016);,  155-165 and \emph{Strongly extensional homomorphism of implicative semigroups with apartness}.  Sarajevo J. Math., 13insert ignore into journalissuearticles values(2);insert ignore into journalissuearticles values(2017);,  155-162);. In this paper, as a continuation of the mentioned articles, the concept of co-ideals was introduced in the implicative semigroups with apartness. Some of the important properties of these substructures in such semigroups have been proven. In addition, it has been shown that the family of all co-ideals in these semigroups forms a complete lattice.
Keywords : Constructive mathematics, semigroup with apartness, co ordered semigroups, implicative semigroups with apartness, co ideals