Geodesic
Free rectangular dibands and free dimonoids
Algebra and discrete mathematics, Tome 11 (2011) no. 2, pp. 92-111.

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We construct a free rectangular diband and describe its structure. We also present the least rectangular diband congruence, the least $(rb,rz)$-congruence, the least left zero and right zero congruence, the least rectangular band congruence and the least left zero congruence on free dimonoids and use them to obtain decompositions of free dimonoids.
Keywords: rectangular dimonoid, free rectangular dimonoid, free dimonoid, diband of subdimonoids. 
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Anatolii V. Zhuchok. Free rectangular dibands and free  dimonoids. Algebra and discrete mathematics, Tome 11 (2011) no. 2, pp. 92-111. http://geodesic.mathdoc.fr/item/ADM_2011_11_2_a6/

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