Several co-associative laws and pre-B-algebras

Siriluk Donganont; Sun Shin Ahn; Hee Sik Kim

doi:10.3934/math.2025431

Several co-associative laws and pre-B-algebras

Siriluk Donganont
, Sun Shin Ahn
, Hee Sik Kim

Department of Mathematics Education

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	9332-9341
Number of pages	10
Journal	AIMS Mathematics
Volume	10
Issue number	4
DOIs	https://doi.org/10.3934/math.2025431
State	Published - 2025

Keywords

anti-commutative
B-algebra
co-associative
d-algebra
post groupoid
pre-B-algebra
pre-semigroup
⊥-algebra

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10.3934/math.2025431

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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 = "anti-commutative, B-algebra, co-associative, d-algebra, post groupoid, pre-B-algebra, pre-semigroup, ⊥-algebra",

author = "Siriluk Donganont and Ahn, \{Sun Shin\} and Kim, \{Hee Sik\}",

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AU - Ahn, Sun Shin

AU - Kim, Hee Sik

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N2 - 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.

AB - 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.

KW - anti-commutative

KW - B-algebra

KW - co-associative

KW - d-algebra

KW - post groupoid

KW - pre-B-algebra

KW - pre-semigroup

KW - ⊥-algebra

UR - https://www.scopus.com/pages/publications/105005116297

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DO - 10.3934/math.2025431

M3 - Article

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SN - 2473-6988

VL - 10

SP - 9332

EP - 9341

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 4

ER -

Several co-associative laws and pre-B-algebras

Abstract

Keywords

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