Free weakly k-nilpotent n-tuple semigroups

Authors

ANATOLII V. ZHUCHOKFollow
JORG KOPPITZFollow

Author ORCID Identifier

ANATOLII ZHUCHOK: 0000-0002-4254-823X

JORG KOPPITZ: 0000-0001-6483-4854

DOI

10.55730/1300-0098.3561

Abstract

In this paper, we construct a free object in the variety of weakly k-nilpotent n-tuple semigroups and characterize the least weakly k-nilpotent congruence on a free n-tuple semigroup. Moreover, we present separately free weakly k-nilpotent n-tuple semigroups of rank 1, calculate the cardinality of the free weakly k-nilpotent n-tuple semigroup for the finite case, emphasize that the semigroups of the free weakly k-nilpotent n-tuple semigroup are isomorphic and the automorphism group of the free weakly k-nilpotent n-tuple semigroup is isomorphic to the symmetric group. We also describe all maximal n-tuple subsemigroups of the free weakly k-nilpotent n-tuple semigroup and all regular elements of the endomorphism semigroup of the free weakly k-nilpotent n-tuple semigroup, and give a criterion for an isomorphism of endomorphism semigroups of free weakly k-nilpotent n-tuple semigroups.

Keywords

n-Tuple semigroup, free weakly k -nilpotent n-tuple semigroup, free n-tuple semigroup, semigroup, congruence

First Page

1067

Last Page

1078

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

ZHUCHOK, ANATOLII V. and KOPPITZ, JORG (2024) "Free weakly k-nilpotent n-tuple semigroups," Turkish Journal of Mathematics: Vol. 48: No. 6, Article 6. https://doi.org/10.55730/1300-0098.3561
Available at: https://journals.tubitak.gov.tr/math/vol48/iss6/6