THE FIRST ISOMORPHISM THEOREM FOR (CO-ORDERED) $\\Gamma$-SEMIGROUPS WITH APARTNESS

Authors : Daniel A. Romano

Pages : 239-253

Doi:10.33773/jum.1195108

View : 35 | Download : 29

Publication Date : 2023-07-31

Article Type : Research Article

Abstract :The notion of $\\Gamma$-semigroups has been introduced by Sen and Saha in 1986. This author introduced the concept of $\\Gamma$-semigroups with apartness and analyzed their properties within the Bishop\'s constructive orientation. Many classical notions and processes of semigroups and $\\Gamma$-semigroups have been extended to $\\Gamma$-semigroups with apartness. Co-ordered $\\Gamma$-semigroups with apartness have been studied by the author also. In this paper, as a continuation of previous research, the author investigates the specificity of two forms of the first isomorphism theorem for (co-ordered) $\\Gamma$-semigroups with apartness which one of them has no a counterpart in the Classical case. In addition, specific techniques used in proofs within algebraic Bishop\'s constructive orientation are exposed.
Keywords : Bishop, Intuitionistic logic, $\\Gamma$-semigroup with apartness, ordered $\\Gamma$-semigroup under co-order, co-congruence in $\\Gamma$-semigroup, the isomorphism theorem.}