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Keywords:
distributive lattice; indecomposable matrix; fully indecomposable matrix; semigroup; characterization
distributive lattice; indecomposable matrix; fully indecomposable matrix; semigroup; characterization
Summary:
In this paper, the concepts of indecomposable matrices and fully indecomposable matrices over a distributive lattice $L$ are introduced, and some algebraic properties of them are obtained. Also, some characterizations of the set $F_n(L)$ of all $n\times n$ fully indecomposable matrices as a subsemigroup of the semigroup $H_n(L)$ of all $n\times n$ Hall matrices over the lattice $L$ are given.
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