Some Conditions for Matrices over an Incline To Be Invertible and General Linear Group on an Incline  

作　　者：Song Chol HAN Hong Xing LI 

机构地区：[1]Department of Mathematics and Mechanics, Kim Il Sung University, Pyongyang, D. P. R. Korea [2]Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2005年第5期1093-1098,共6页数学学报（英文版）

基　　金：National Natural Science Foundation of China （60174013）; Research Foundation for Doctoral Program of Higher Education （20020027013）; Science and Technology Key Project Foundation of Ministry of Education （03184） ; Major State Basic Research Development Program of China （2002CB312200）

摘　　要：Inclines are the additively idempotent semirings in which products are less than or equal to either factor. In this paper, some necessary and sufficient conditions for a matrix over L to be invertible are given, where L is an incline with 0 and 1. Also it is proved that L is an integral incline if and only if GLn（L） = PLn （L） for any n （n 〉 2）, in which GLn（L） is the group of all n × n invertible matrices over L and PLn（L） is the group of all n × n permutation matrices over L. These results should be regarded as the generalizations and developments of the previous results on the invertible matrices over a distributive lattice.Inclines are the additively idempotent semirings in which products are less than or equal to either factor. In this paper, some necessary and sufficient conditions for a matrix over L to be invertible are given, where L is an incline with 0 and 1. Also it is proved that L is an integral incline if and only if GLn（L） = PLn （L） for any n （n 〉 2）, in which GLn（L） is the group of all n × n invertible matrices over L and PLn（L） is the group of all n × n permutation matrices over L. These results should be regarded as the generalizations and developments of the previous results on the invertible matrices over a distributive lattice.

关 键 词：INCLINE Distributive lattice Invertible matrix Permutation matrix Linear group 

分 类 号：O152.3[理学—数学]