jum

Journal of Universal Mathematics

2618-5660 2618-5660

Gökhan ÇUVALCIOĞLU

10.33773/jum.1195108

Mathematical Sciences

Matematik

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

https://orcid.org/0000-0003-1148-3258

Romano

Daniel A.

International Mathematical Virtual Institute, 78000 Banja Luka, Bosnia and Herzegovina

07 31 2023

6 2 239 253 10 26 2022 07 31 2023

2018

Journal of Universal Mathematics

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 analyzedtheir 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.

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