Geodesic
On applications of associativity of dual compositions in the algebra of Boolean matrices
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 4, pp. 181-192.

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We consider matrices of arbitrary size with elements from an arbitrary Boolean algebra with two partial multiplications that are defined in a dual way and are not associative with respect to each other in the general case. We show the connection of solvability of the simplest matrix equations, the matrix regularity, and the belonging to one-sided principal ideals with associativity of some dual compositions. 
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V. B. Poplavski. On applications of associativity of dual compositions in the algebra of Boolean matrices. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 4, pp. 181-192. http://geodesic.mathdoc.fr/item/FPM_2012_17_4_a10/

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