Interassociativity and three-element doppelsemigroups
Group Theory
2020-04-07 v1 Rings and Algebras
Abstract
In the paper we characterize all interassociates of some non-inverse semigroups and describe up to isomorphism all three-element (strong) doppelsemigroups and their automorphism groups. We prove that there exist pairwise non-isomorphic three-element doppelsemigroups among which doppelsemigroups are commutative. Non-commutative doppelsemigroups are divided into pairs of dual doppelsemigroups. Also up to isomorphism there are strong doppelsemigroups of order , and all non-strong doppelsemigroups are not commutative.
Cite
@article{arxiv.2004.02505,
title = {Interassociativity and three-element doppelsemigroups},
author = {Volodymyr Gavrylkiv and Diana Rendziak},
journal= {arXiv preprint arXiv:2004.02505},
year = {2020}
}