Geodesic
Factorization properties of $(n\times n)$ Boolean matrices
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 5, pp. 155-164.

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It is proved that every $(n\times n)$ Boolean matrix can be expressed as a product of primes and elementary matrices in the semigroup of Boolean matrices. 
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E. E. Marenich. Factorization properties of $(n\times n)$ Boolean matrices. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 5, pp. 155-164. http://geodesic.mathdoc.fr/item/FPM_2008_14_5_a9/

[1] Borosh J., Hartfiel D. J., Maxson C. J., “Answer to questions posed by Richman and Schneider”, Linear and Multilinear Algebra, 3 (1976), 255–258 | DOI | MR | Zbl

[2] De Caen D., Gregory D. A., “Primes in the semigroup of Boolean matrices”, Linear Algebra Appl., 37 (1981), 119–134 | DOI | MR | Zbl

[3] De Caen D., Gregory D. A., Pullman N. J., “The Boolean rank of zero-one matrices”, Combinatorics and Computing, Proc. 3rd Caribb. Conf. on Combinatorics, Graph Theory, and Computing (Cave Hill, Barbados, 1981), 1981, 169–173 | MR | Zbl

[4] Cho H. H., “Prime Boolean matrices and factorizations”, Linear Algebra Appl., 190 (1993), 87–98 | DOI | MR | Zbl

[5] Cho H. H., “Permanents of prime Boolean matrices”, Bull. Korean Math. Soc., 35:3 (1998), 605–613 | MR | Zbl

[6] Devadze H. M., “Generating sets of semigroups of all binary relations in a finite set”, Dokl. Akad. Nauk BSSR, 12 (1968), 765–768 | MR | Zbl

[7] Gregory D. A., Pullman N. J., “Prime Boolean matrices, a graph theoretic approach”, Ars Combinatoria, 12 (1981), 81–110 | MR | Zbl

[8] Gregory D. A., Pullman N. J., “Semiring rank: Boolean rank and nonnegative rank factorization”, J. Combin. Inform. System Sci., 8:3 (1983), 223–233 | MR | Zbl

[9] Kim K. H., Boolean Matrix Theory and Its Applications, Marcel Dekker, New York, 1982 | MR | Zbl

[10] Richman D. J., Schneider H., “Primes in the semigroup of nonnegative matrices”, Linear and Multilinear Algebra, 2 (1974), 135–140 | DOI | MR | Zbl

[11] Tchuente M., On the Decomposition of Boolean Matrices, Univ. of Grenoble, Grenoble, 1980