Geodesic
On the properties of Boolean matrices
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 4, pp. 137-142

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We consider the partial semigroup of Boolean matrices of various finite sizes under the operations of conjunctive and disjoint multiplication. We estimate the possible number of vectors in the row basis and column basis. The subminimal, subsubminimal and submaximal in general sense $\mathscr D$-classes are found. The properties of secondary idempotents are investigated. A conjecture of recursive construction of the reduced matrices is suggested. 
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     title = {On the properties of {Boolean} matrices},
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O. O. Shchekaturova; V. A. Yaroshevich. On the properties of Boolean matrices. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 4, pp. 137-142. http://geodesic.mathdoc.fr/item/ISU_2013_13_4_a24/