|本期目录/Table of Contents|

[1]毛小燕,特木尔朝鲁*.低阶CA-广群及其分类[J].宁波大学学报(理工版),2020,33(3):63-68.
 MAO Xiaoyan,TEMUER Chaolu*.Low-order CA-groupoids and resulting classification[J].Journal of Ningbo University(Natural Science & Engineering Edition),2020,33(3):63-68.
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《宁波大学学报》(理工版)[ISSN:1001-5132/CN:33-1134/N]

卷:
第33卷
期数:
2020年3期
页码:
63-68
栏目:
出版日期:
2020-05-10

文章信息/Info

Title:
Low-order CA-groupoids and resulting classification
作者:
毛小燕12 特木尔朝鲁2*
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
Author(s):
MAO Xiaoyan12 TEMUER Chaolu2*
1.College of Information Engineering, College of Science and Technology of Ningbo University, Ningbo 315300, China;2.College of Arts and Sciences, Shanghai Maritime University, Shanghai 201306, China
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
Keywords:
cyclic associative grouplid (CA-grouplid) neutrosophic extended triplet group (NETG) CA-NET- groupoid classification
分类号:
O152.7
DOI:
-
文献标志码:
A
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CA- AG-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.
Abstract:
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.

参考文献/References:

[1] Boruvka O. Foundations of the Theory of Groupoids and Groups[M]. Berlin: Deutscher Verlag der Wissenschaften, 1974.
[2] Hall T E. On regular semigroups[J]. Journal of Algebra, 1973, 24(1):1-24.
[3] Akinmoyewa J T. A study of some properties of generalized groups[J]. Octogon Mathematical Magazine, 2009, 17(2):599-626.
[4] Smarandache F, Ali M. Neutrosophic triplet group[J]. Neural Computing & Applications, 2018, 29(7):595-601.
[5] Stevanovic N, Protic P V. Some decompositions on Abel-Grassmann’s groupoids[J]. Pure Mathematics and Applications, 1997, 8(2):355-366.
[6] Zhang X H, Ma Z R, Yuan W T. Cyclic associative groupoids (CA-groupoids) and cyclic associative neutrosophic extended triplet groupoids[J]. Neutrosophic Sets and Systems, 2019, 29:19-29.
[7] Sholander M. Medians, lattices, and trees[J]. Proceedings of the American Mathematical Society, 1954, 5(5):808- 812.
[8] Kleinfeld M. Rings with x(yz)=y(zx)[J]. Communications in Algebra, 1995, 23(13):5085-5093.
[9] 詹建明, 谭志松. 左弱Novikov代数[J]. 数学杂志, 2005, 25(2):135-138.
[10] Behn A, Correa I, Hentzel I R. Semiprimality and nilpotency of nonassociative rings satisfying x(yz)= y(zx)[J]. Communications in Algebra, 2008, 36(1):132- 141.
[11] Iqbal M, Ahmad I, Shah M, et al. On cyclic associative Abel-Grassman groupoids[J]. British Journal of Mathe- matics & computer Science, 2016, 12(5):1-16.
[12] 李宪年, 宋子伦. 轮广群[J]. 陕西工学院学报, 2001, 17(4):61-63.
[13] Keedwell A D, J. Dénes J. Latin Squares and Their Applications[M]. Akademia kiado, Hungary, Budepest, 1974.
[14] Kazim M, Nasseerudin M. On almost semigroup[J]. Alig Bull Math, 1972, 2:1-7.
[15] Holgate P. Groupoids satisfying simple intertive law[J]. Math Student, 1992, 61:101-104.
[16] Mushtaq Q, Iqbal Q. Decomposition of a locally associative LA-semigroup[J]. Semigroup Forum, 1990, 41:155-164.
[17] Dudek W A, Gigon R S. Completely inverse AG**- groupoids[J]. Semigroup Forum, 2013, 76:107-123.
[18] Howie J M. Fundamentals of Semigroup Theory[M]. Oxford: Oxford University Press, 1995.
[19] Zhang X H, Wu X Y, Mao X Y, et al. On neutrosophic extended triplet groups (loops) and Abel-Grassmann’s groupoids (AG-groupoids)[J]. Journal of Intelligent & Fuzzy Systems, 2019, 37:5743-5753.
[20] Zhang X H, Mao X Y, Smarandache F, Park C. On homomorphism theorem for perfect neutrosophic extended triplet groups[J]. Information, 2018, 9(9):237- 248.
[21] Zhang X H, Mao X Y, Wu Y T, et al. Neutrosophic filters in Pseudo-BCI algebras[J]. International Journal for Uncertainty Quantification, 2018, 8(6):511-526.
[22] Mao X Y, Zhou H J. Classification of proper hyper BCI-algebras of order 3[J]. Applied Mathematics & Information Sciences, 2015(1):387-393.
[23] 毛小燕, 张小红, 周晖杰. 元素个数不超过6的真伪BCK-代数[J]. 模糊系统与数学, 2013(6):105-115.
[24] Iqbal M, Ahmad I. Some congruences on CA-AG- groupoids[J]. Punjab University Journal of Mathematics, 2019, 51(3):71-87.
[25] Yuan W T, Zhang X H. Regular CA-groupoids and cyclic associative neutrosophic extended triplet groupoids (CA- NET-groupoids) with green relations[J]. Mathematics, 2020, 8(2):204-224.
[26] Ma Z R, Zhang X H, Smarandache F. Some results on various cancellative CA-Groupoids and variant CA- groupoids[J]. Symmetry, 2020, 12(2):315-335.

备注/Memo

备注/Memo:
收稿日期:2020-01-29.宁波大学学报(理工版)网址:http://journallg.nbu.edu.cn/
基金项目: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).
第一作者:毛小燕(1980-),女,浙江衢州人,讲师,主要研究方向:代数学、复杂信息决策理论与方法.E-mail:maoxiaoyan@nbu.edu.cn
*通信作者:特木尔朝鲁(1962-),男,蒙古族,内蒙古通辽人,教授,主要研究方向:力学.E-mail:tmchaolu@shmtu.edu.cn
更新日期/Last Update: 2020-05-06