The zero divisor and augmentation conjectures for medial quandle rings

Luc Ta

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arXiv · 2610.20306

The zero divisor and augmentation conjectures for medial quandle rings

Luc Ta

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Abstract

For quandle rings, Bardakov--Passi--Singh and Elhamdadi--Nunez--Singh respectively formulated an analogue of Kaplansky's zero divisor conjecture and a weakened analogue of Kaplansky's idempotent conjecture involving the augmentation map. In this note, we verify these conjectures for medial quandles. The latter holds for a larger class of quandles; we characterize integral domains over which the statement holds for this class. We also characterize integral domains of characteristic 0 over which the statement holds for a given finite Alexander quandle.

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BibTeX RIS

Luc Ta. 2026-10-14. The zero divisor and augmentation conjectures for medial quandle rings. https://arxiv.org/abs/2610.20306

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