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On the potential divisibility of matrices over distributive lattices
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I. B. Kozhukhov
Published/Copyright:
July 8, 2010
Abstract
We consider matrices of arbitrary sizes (including infinite matrices) over a distributive lattice L and prove that if L = 2X is a lattice of all subsets of a set X, then the potential divisibility of matrices (from the left or from the right) of one of the matrices by the other matrix is equivalent to the usual divisibility. In particular, in the semigroup of square matrices over the lattice 2X the Green relation ℒ coincides with the generalised Green relation ℒ*
Received: 2009-06-01
Published Online: 2010-07-08
Published in Print: 2010-July
© de Gruyter 2010
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Articles in the same Issue
- A limit theorem for the logarithm of the order of a random A-permutation
- On game-theoretic characterisation of stochastic independence
- On the potential divisibility of matrices over distributive lattices
- On learning monotone Boolean functions with irrelevant variables
- Barriers of perfectly balanced Boolean functions
- On the classification of Post automaton bases by the decidability of the A-completeness property for definite automata
