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. 
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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. https://geodesic-test.mathdoc.fr/item/BASM_2020_3_a2/

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