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

Öz

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.

Anahtar Kelimeler

• 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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