Geodesic
On idempotents of algebra of Boolean matrices
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 12 (2012) no. 2, pp. 26-33

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The structure of idempotent matrices in partial semigroups of matrices of arbitrary sizes with elements from arbitrary Boolean algebra with conjunctive and disjunctive partial multiplications is investigated. The connection of solvability of the simplest matrix equations with some kind of idempotent matrices which are called “secondary idempotents” is shown. Also we show the connection of arbitrary idempotent matrices with secondary idempotents and investigate their properties. 
@article{ISU_2012_12_2_a4,
     author = {V. B. Poplavski},
     title = {On idempotents of  algebra of  {Boolean} matrices},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {26--33},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2012_12_2_a4/}
}
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V. B. Poplavski. On idempotents of  algebra of  Boolean matrices. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 12 (2012) no. 2, pp. 26-33. http://geodesic.mathdoc.fr/item/ISU_2012_12_2_a4/