Geodesic
Free $n$-nilpotent dimonoids
Algebra and discrete mathematics, Tome 16 (2013) no. 2, pp. 299-310

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We construct a free $n$-nilpotent dimonoid and describe its structure. We also characterize the least $n$-nilpotent congruence on a free dimonoid, construct a new class of dimonoids with zero and give examples of nilpotent dimonoids of nilpotency index $2$.
Keywords: $n$-nilpotent dimonoid, free $n$-nilpotent dimonoid, $0$-diband of subdimonoids, dimonoid, semigroup. 
@article{ADM_2013_16_2_a11,
     author = {A. V. Zhuchok},
     title = {Free $n$-nilpotent dimonoids},
     journal = {Algebra and discrete mathematics},
     pages = {299--310},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2013_16_2_a11/}
}
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A. V. Zhuchok. Free $n$-nilpotent dimonoids. Algebra and discrete mathematics, Tome 16 (2013) no. 2, pp. 299-310. http://geodesic.mathdoc.fr/item/ADM_2013_16_2_a11/