Endomorphisms of free Steiner quasigroups

Silvia Barbina; Enrique Casanovas

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arXiv · 2412.06055

Endomorphisms of free Steiner quasigroups

Silvia Barbina·Enrique Casanovas

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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 $M$ 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.

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Silvia Barbina, Enrique Casanovas. 2024-12-08. Endomorphisms of free Steiner quasigroups. https://arxiv.org/abs/2412.06055

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