Abstract
In this paper, nilpotent matrices over distributive lattices are considered. Some properties and characterizations for nilpotent matrices are established and in particular, a necessary and sufficient condition for an n × n nilpotent matrix to have the nilpotent index n is given. Also, some properties of the reduction of a nilpotent matrix are obtained. Partial results obtained in this paper are results on nilpotent fuzzy matrices by H. Hashimoto.
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