矩阵中的胞腔半群代数

Semigroup Algebras with Cellularity in Matrices

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.