Geodesic
Free left $k$-nilpotent $n$-tuple semigroups
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2020), pp. 29-38

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We introduce left (right) $k$-nilpotent $n$-tuple semigroups which are analogs of left (right) nilpotent semigroups of rank $p$ considered by Schein, and construct the free left (right) $k$-nilpotent $n$-tuple semigroup of rank $1$. We prove that the free left (right) $k$-nilpotent $n$-tuple semigroup of rank $m>1$ is a subdirect product of the free left (right) $k$-nilpotent semigroup with $m$ generators and the free left (right) $k$-nilpotent $n$-tuple semigroup of rank $1$. We also characterize the least left (right) $k$-nilpotent congruence on the free $n$-tuple semigroup. 
@article{BASM_2020_3_a2,
     author = {Anatolii V. Zhuchok and Yuliia V. Zhuchok and Oksana O. Odintsova},
     title = {Free left $k$-nilpotent $n$-tuple semigroups},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {29--38},
     publisher = {mathdoc},
     number = {3},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2020_3_a2/}
}
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Anatolii V. Zhuchok; Yuliia V. Zhuchok; Oksana O. Odintsova. Free left $k$-nilpotent $n$-tuple semigroups. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2020), pp. 29-38. http://geodesic.mathdoc.fr/item/BASM_2020_3_a2/