分配伪格上的可逆矩阵

摘要

A complete description of the invertible matrices over a distributive pseudo-lattice is given, some necessary and sufficient conditions for a matrix over a distributive pseudo-lattices to be invertible are obtained. Moreover, it is proved that a matrix is invertible if and only if it is a permutation matrix over an integral distributive pseudo-lattice. These results can be regarded as generalizations of the previous results on the invertible matrices over distributive lattices and commutative inclines.%本文介绍了分配伪格上的可逆矩阵,获得分配伪格上矩阵可逆的一些充分必要条件,也证明了在整的分配伪格上,矩阵可逆当且仅当它是一个置换矩阵.这些结果推广了分配格和交换坡上已有关于可逆矩阵的结果.