| Some Conditions for Matrices over an Incline To Be Invertible and General Linear Group on an Incline |
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| 作者姓名： | Song Chol HAN Hong Xing LI |
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| 作者单位： | [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 |
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| 基金项目： | Supported by 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） and Major State Basic Research Development Program of China （2002CB312200） |
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| 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.
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| 关 键 词： | 线性群 分布式格子 倒转矩阵 交换矩阵 倾斜角 |
| 收稿时间： | 2002-12-20 |
| 修稿时间： | 2002-12-202004-03-16 |
Some Conditions for Matrices over an Incline To Be Invertible
and General Linear Group on an Incline |
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| Song Chol HAN Hong Xing LI.Some Conditions for Matrices over an Incline To Be Invertible and General Linear Group on an Incline[J].Acta Mathematica Sinica,2005,21(5):1093-1098. |
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| Authors: | Song Chol Han Hong Xing Li |
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| Institution: | (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;(3) Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China |
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| Abstract: | 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 GL
n
(L) = PL
n
(L) for any n (n ≥ 2), in which GL
n
(L) is the group of all n × n invertible
matrices over L and PL
n
(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.
Supported by 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) and Major State Basic Research Development Program of China (2002CB312200) |
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| Keywords: | Incline Distributive lattice Invertible matrix Permutation matrix Linear group |
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