TY  - JOUR
T1  - THE FIRST ISOMORPHISM THEOREM FOR  (CO-ORDERED) $\Gamma$-SEMIGROUPS WITH APARTNESS
AU  - Romano, Daniel A.
PY  - 2023
DA  - July
Y2  - 2023
DO  - 10.33773/jum.1195108
JF  - Journal of Universal Mathematics
JO  - JUM
PB  - Gökhan ÇUVALCIOĞLU
WT  - DergiPark
SN  - 2618-5660
SP  - 239
EP  - 253
VL  - 6
IS  - 2
LA  - en
AB  - 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.
KW  - Bishop
KW  - Intuitionistic logic
KW  - $\Gamma$-semigroup with
apartness
KW  - ordered $\Gamma$-semigroup under co-order
KW  - co-congruence in $\Gamma$-semigroup
KW  - the isomorphism theorem.}
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UR  - https://doi.org/10.33773/jum.1195108
L1  - https://dergipark.org.tr/en/download/article-file/2733130
ER  -