Free left k-nilpotent n-tuple semigroups
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512.534+512.54+512.554 (1)
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ZHUCHOK, Anatolii, ZHUCHOK, Yuliia, ODINTSOVA, Oksana O.. Free left k-nilpotent n-tuple semigroups. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2020, nr. 3(94), pp. 29-38. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 3(94) / 2020 / ISSN 1024-7696 /ISSNe 2587-4322

Free left k-nilpotent n-tuple semigroups

CZU: 512.534+512.54+512.554
MSC 2010: 08B20, 20M10, 20M99, 17A30.

Pag. 29-38

Zhuchok Anatolii1, Zhuchok Yuliia1, Odintsova Oksana O.2
 
1 Taras Shevchenko National University of Kyiv,
2 Sumy State Pedagogical University named after A. S. Makarenko
 
 
Disponibil în IBN: 24 august 2021


Rezumat

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.

Cuvinte-cheie
n-tuple semigroup, free left k-nilpotent n-tuple semigroup, free n-tuple semigroup, semigroup, congruence

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