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IMI/Publicaţii/BASM/Ediţii/BASM n.3(94), 2020/

Free left k-nilpotent n-tuple semigroups

Authors: Anatolii V. Zhuchok, Yuliia V. Zhuchok, Oksana O. Odintsova

Abstract

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.

Anatolii V. Zhuchok, Yuliia V. Zhuchok
Department of Algebra and System Analysis, Luhansk
Taras Shevchenko National University, Gogol square, 1,
Starobilsk 92703, Ukraine
E-mail: ,

Oksana O. Odintsova
Department of Mathematics, ”A. S. Makarenko” Sumy
State Pedagogical University, street Romenska, 87, Sumy
40002, Ukraine
E-mail:

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