Semilattice Co-Congruence in $\Gamma$-Semigroups

Abstract

As a generalization of semigroups, Sen, in 1981, introduced the concept of $\Gamma$-semigroups. In the author's paper (D A. Romano. $\Gamma$-semigroups with apartness. \emph{Bull. Allahabad Math. Soc.}, 34(1)(2019), 71--83.) it is introduced and analyzed the concept of $\Gamma$-semigroups with apartness in Bishop's constructive framework. In this article, as a continuation of previous research, the concept of co-congruences in $\Gamma$-semigroups is introduced and analyzed. Additionally, it is investigated (co-ordered) semilattice co-congruence on (co-ordered) $\Gamma$-semigroup with apartness.

Keywords

• Bishop’s constructive algebra
• Intuitionistic logic
• $\Gamma$-semigroup with apartness
• Ordered $\Gamma$-semigroup under co-order
• Co-congruence in $\Gamma$-semigroup
• Semillatice co-congruence

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