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arXiv · 2602.08875

On medial Latin quandles and affine modules

Luc Ta
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Abstract

In this note, we show that the category of Latin (resp. commutative) medial quandles is equivalent to the category of affine modules over a certain Laurent polynomial ring (resp. the dyadic rationals). As applications, we describe free objects in these categories and obtain a structure theorem for finitely generated medial commutative quandles. We also characterize racks whose duals are commutative. Collectively, this solves two open problems of Bardakov and Elhamdadi (arXiv:2601.07057).

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Luc Ta. 2026-02-09. On medial Latin quandles and affine modules. https://doi.org/10.4153/s0008439526102306

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