In this paper, the concepts of indecomposable matrices and fully indecomposable matrices over a distributive lattice are introduced, and some algebraic properties of them are obtained. Also, some characterizations of the set of all fully indecomposable matrices as a subsemigroup of the semigroup of all Hall matrices over the lattice are given.
Let be a positive integer, and the set of all
-circulant matrices over the Boolean algebra , . For any fixed -circulant matrix () in , we define an operation “” in as follows: for any in , where is the usual product of Boolean matrices. Then is a semigroup. We denote this semigroup by and call it the sandwich semigroup of generalized circulant Boolean matrices with sandwich matrix . Let be an idempotent element in and the maximal subgroup in containing...
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