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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.

MSC:

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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