Endomorphisms of free Steiner quasigroups
Logic
2025-11-10 v3
Abstract
A free Steiner quasigroup is a free object in the variety of Steiner quasigroups. Free Steiner quasigroups are characterised by the existence of a levelled construction that starts with a free base - that is, a set of elements none of which is a product of the others, and which generate the quasigroup. Then each element in a free Steiner quasigroup can be obtained as a term on the free base. We characterise homomorphisms between substructures of a free Steiner quasigroup where one generator is replaced by a term in the original generators. The characterisation depends on certain synctactic properties of the term in question.
Cite
@article{arxiv.2412.06055,
title = {Endomorphisms of free Steiner quasigroups},
author = {Silvia Barbina and Enrique Casanovas},
journal= {arXiv preprint arXiv:2412.06055},
year = {2025}
}