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

Year 2023, Volume: 6 Issue: 2, 239 - 253, 31.07.2023

Daniel A. Romano

https://doi.org/10.33773/jum.1195108

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.}

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