低阶CA-广群及其分类  

Low-order CA-groupoids and resulting classification

作　　者：毛小燕 特木尔朝鲁[2] MAO Xiaoyan;TEMUER Chaolu(College of Information Engineering,College of Science and Technology of Ningbo University,Ningbo 315300,China;College of Arts and Sciences,Shanghai Maritime University,Shanghai 201306,China)

机构地区：[1]宁波大学科学技术学院信息工程学院,浙江宁波315300 [2]上海海事大学文理学院,上海201306

出　　处：《宁波大学学报（理工版）》2020年第3期63-68,共6页Journal of Ningbo University：Natural Science and Engineering Edition

基　　金：浙江省自然科学基金(LY20A010012);宁波市横向课题(汽车爆胎自救辅助装置报警系统建模、仿真、开发及评估).

摘　　要：群是描述基于结合律的对称性的基本代数结构.为了表达更一般的对称性(或变异对称性),群的概念被以各种方式推广.循环结合广群(CA-广群)是以非结合环、左弱Novikov代数和CAAG-广群为背景,基于循环结合律的代数结构,对于探讨低阶CA-广群及其分类进而深入研究CA-广群具有重要意义.本文介绍了CA-广群、中智扩展三元组群(NET-群)等基本概念及其基本性质,并借助Matlab软件设计计算程序得到了全部3阶和4阶不同构的CA-广群,也给出其完全分类.Group is the basic algebraic structure that describes symmetry based on associative law.In order to express more general symmetry(or variation symmetry),the concept of group is generalized in various ways.Cyclic associative groupoid(CA-groupoid) is the concept proposed based on the law of cyclic association and the background of non-associative ring,left weakly Novikov algebra and CA-AG-groupoid.It is of great significance to explore low-order CA-groupoid and their classification for the further study of CA-groupoid.In this paper the basic concepts are first introduced,and the triplet group(NETG) is extended with properties of CA-groupoids and neutrosophic.Next,a calculation program is designed using Matlab software to obtain all non-isomorphic CA-groupoids of order 3 and order 4.Finally the complete classification is determined.

关 键 词：循环结合广群(CA-广群) 中智扩展三元组群(NET-群) CA-NET-广群 分类 

分 类 号：O152.7[理学—数学]