Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Ta, Luc
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221912456