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Some Conditions for Matrices over an Incline To Be Invertible and General Linear Group on an Incline 被引量:1
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作者 Song Chol HAN Hong Xing LI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2005年第5期1093-1098,共6页
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... 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. 展开更多
关键词 INCLINE Distributive lattice Invertible matrix Permutation matrix Linear group
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