Indecomposable matrices over a distributive lattice. (English) Zbl 1164.15326

Summary: 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.


15B33 Matrices over special rings (quaternions, finite fields, etc.)
15A18 Eigenvalues, singular values, and eigenvectors
06D05 Structure and representation theory of distributive lattices
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