Turkish Journal of Mathematics
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.
DOI
10.55730/1300-0098.3561
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, A. V, & KOPPITZ, J (2024). Free weakly k-nilpotent n-tuple semigroups. Turkish Journal of Mathematics 48 (6): 1067-1078. https://doi.org/10.55730/1300-0098.3561
