Finite {\bf $\Gamma$-AG}-groupoids with Left Identities and Left Zeros
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i3.6172Keywords:
AG-groupoid, $\Gamma$-AG-groupoid, semigroup, $\Gamma$-semigroup, groupAbstract
Let Γ be a nonempty set. A nonempty set A is called a Γ-AG-groupoid if there is a function f of A × Γ × A into A, customary denoted aγb for f(a, γ, b), satisfying the identity (aγb)βc = (cγb)βa for any a, b, c ∈ A and γ, β ∈ Γ. For each γ ∈ Γ, an operation on A associated to γ is given by ab = aγb. Suppose further that A is finite, contains a left identity and a left zero a0. The objective of this paper is to provide sufficient conditions under which the set A \ {a0} is a commutative group under the operation on A determined by γ for all γ ∈ Γ.
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Copyright (c) 2025 Cholathorn Chanoi, Apichaya Kauppamung, Panuwat Luangchaisri, Thawhat Changphas
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