On Co-Ideals of Implicative Semigroups with Apartness

Year 2019, Volume: 11 Issue: 2, 101 - 106, 31.12.2019

Daniel A. Romano

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 (\emph{An introduction to implicative semigroups with apartness}, Sarajevo J. Math., 12(25)(2)(2016),  155-165 and \emph{Strongly extensional homomorphism of implicative semigroups with apartness}.  Sarajevo J. Math., 13(2)(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

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