Abstract

This paper introduces a new concept called cyclic associative semihypergroup (CA-semihypergroup). The relationships among CA-semihypergroups, Semihypergroups and LA-semihypergroups are studied through some interesting examples. The relationships among various NET-CA-semihypergroups are also studied. The main properties of strong pure neutrosophic extended triplet CA-semihypergroups (SP-NET-CA-semihypergroups) are obtained. In particular, the algorithm of a generated CA-semihypergroup of order tm+n by two known CA-semihypergroups of order m and n is proven, and a CA-semihypergroup of order 19 is obtained by using a Python program. Moreover, it is proven that five different definitions, which can all be used as the definition of SP-NET-CA-Semihypergroup, are equivalent.

Highlights

  • The associative law Citation: Hu, M.; Zhang, X

  • Building on the achievements of our predecessors, in this paper we mainly study a class of binary hypergroupoids with cyclic associative law, which is called CA-semihypergroup

  • The concepts of various CA-semihypergroups are introduced for the first time in this paper

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Summary

Introduction

This paper examines a type of nonassociative algebraic structure with cyclic associative law. Cyclic associative law is used to study other algebraic structures. Shah and M.I. Ali defined AG-groupoids with cyclic associative law (CA-AG-groupoid) and studied their properties (see [15]). A year later, Yuan W.T., and Zhang, X.H. studied CA-NET-Groupoids with Green relations and proved some important results (see [19]). Smarandache and X.H. Zhang studied the properties and construction methods of an SP-NET-LA-semihypergroup and found that the symmetry of this algebraic structure is not perfect (see [23]). Building on the achievements of our predecessors, in this paper we mainly study a class of binary hypergroupoids with cyclic associative law, which is called CA-semihypergroup. If we replace cyclic associative law with left invertive law, (C, ?) is said to be an LA-semihypergroup.

The binary hyperoperation
A CA-semihypergroup
14. How how we Remark
Findings
Conclusions
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