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Research Article | Open Access

Several co-associative laws and pre- B-algebras

Siriluk Donganont1, Sun Shin Ahn2, Hee Sik Kim3( )
School of Sciences, University of Phayao, Phayao 56000, Thailand
Department of Mathematics Education, Dongguk University, Seoul 04620, Korea
Department of Mathematics, Hanyang University, Seoul 04763, Korea
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Abstract

In this paper, we introduce several co-associative laws and the notion of a pre- B-algebra. We show that every B-algebra is both a pre- B-algebra and a ⊥-algebra. We apply the notions of a post groupoid and a pre-semigroup of a groupoid to the set ( N , + ) of all nonnegative integers, and we prove that the groupoid ( N , + ) cannot be a post groupoid of a B-algebra or an edge d-algebra.

Keywords

pre-B-algebraB-algebrad-algebraco-associative⊥-algebraanti-commutativepost groupoidpre-semigroup
CLC number: 06F35, 20N02

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AIMS Mathematics
Volume 10 Issue 4,
April 2025
Pages 9332-9341
DOI: 10.3934/math.2025431

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Donganont S, Ahn SS, Kim HS. Several co-associative laws and pre- B-algebras. AIMS Mathematics, 2025, 10(4): 9332-9341. https://doi.org/10.3934/math.2025431

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Received: 11 September 2024
Revised: 31 March 2025
Accepted: 17 April 2025
Published: 15 April 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)