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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...
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