## 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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### References:

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