左剩余格序广群上的矩阵方程(英文)

Matrix Equations in Left ResiduatedLattice-ordered Groupoids

研究左剩余格序广群L上矩阵方程AX=B的解集以及所有n阶矩阵的集合Mn(L),将文献[3]中的一切结果推广到左剩余格序广群上,而且证明了若L是左剩余格序广群,则Mn(L)也组成左剩余格序广群。此外,还指出了文献[1]中主要结论的错误。

This paper studies the solution sets of matrix equations AX = B and the set M.（L） of all n × n matrices in lrl-groupoids L. All results stated by Di Nola ＆ Lettieri[a] over left reslduated complete lattices are generalized to the setting of lrl-groupoids. It is proved that Mn（L） forms an lrl-groupoid if L is an lrl-groupoid. The main results of Cheng [1] in residue semislopes are pointed out being faulty.