矩阵中的胞腔半群代数  

Semigroup Algebras with Cellularity in Matrices

作　　者：苏志荣 赵丽云 SU Zhi-rong;ZHAO Li-yun(School of Mathematics and Statistics,Guangdong University of Technology,Guangzhou 510520,China)

机构地区：[1]广东工业大学数学与统计学院,广东广州510520

出　　处：《兰州文理学院学报（自然科学版）》2022年第6期1-7,共7页Journal of Lanzhou University of Arts and Science(Natural Sciences)

摘　　要：在部分常见矩阵以及幻方矩阵的相关定义的基础上,新定义了数独幻方矩阵的概念,从而丰富了幻方矩阵的内容,并且研究了部分常见矩阵以及幻方矩阵的半群系统,还证明了部分常见矩阵半群代数具有胞腔性,以及在特定的条件下,探究了积幻方矩阵半群代数与胞腔代数之间的联系,最后给出了矩阵中的胞腔正则半群代数的一个构造方法.On the basis of the definitions of some common matrices and magic square matrices,the concept of Sudoku magic square matrix is defined,which enriches the content of magic square matrices.The semigroup systems of some common matrices and magic square matrices are studied,and it is proved that some common matrix semigroup algebras have cell cavity.Under certain conditions,the relationship between the semigroup algebras of product magic square matrices and cell cavity algebras is explored.Finally,a construction method of cell cavity regular semigroup algebras in matrices is given.

关 键 词：胞腔代数 半群 矩阵 

分 类 号：O152[理学—数学]