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Organizers |
Ring Theoretic Aspects of Quandles.
by
Mohamed Elhamdadi
University of South Florida
Coauthors: N. Fernando and B. Tsvelikhovskiy.
In a recent paper arXiv:1709.03069 Bardakov et al. initiated the study of quandle rings and posed some open problems. We will start the talk by giving some basic properties of these rings, we will explain how one obtains a complete description of right ideals under the assumption that the inner automorphism group Inn(X) acts orbit 2-transitively on X. We will show that if for two quandles X and Y the inner automorphism groups act 2-transitively and k[X] is isomorphic to k[Y ], then the quandles are of the same partition type. We will also give explicit examples when the quandle rings k[X] and k[Y ] are isomorphic, but the quandles X and Y are not isomorphic, thus solving some open problems in the paper by Bardakov et al.
Date received: November 14, 2018
Copyright © 2018 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbpq-13.