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

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Journal of Universal Mathematics
Volume:6 Issue:2
THE FIRST ISOMORPHISM THEOREM FOR (CO-ORDERED) $\\Gamma$-SEMIGROUPS WITH APARTNESS

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

Pages : 239-253

View : 37 | Download : 40

Publication Date : 2023-07-31

Article Type : Research Paper

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 insert ignore into journalissuearticles values(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

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