论文标题
矩阵乘以晶格
Multiplication of matrices over lattices
论文作者
论文摘要
我们研究方形矩阵在晶格上的乘法操作。如果底层晶格是分布的，则矩阵形成一个半群。我们研究了此矩阵半群的基本元素和nilpotent元素以及最大亚组。我们证明，非分配晶格上的矩阵乘法是反相邻的，并且我们确定晶格的最少或最大元素是不可可理的情况下的可逆矩阵。
We study the multiplication operation of square matrices over lattices. If the underlying lattice is distributive, then matrices form a semigroup; we investigate idempotent and nilpotent elements and the maximal subgroups of this matrix semigroup. We prove that matrix multiplication over nondistributive lattices is antiassociative, and we determine the invertible matrices in the case when the least or the greatest element of the lattice is irreducible.
