Abstract
The paper develops the theory of quandle rings introduced by the authors in a recent work. Orderability of quandles is investigated and many interesting examples of such quandles are given. It is proved that quandle rings of left or right orderable quandles which are semi-latin have no zero-divisors. Idempotents in quandle rings of certain interesting quandles are computed and used to determine sets of maximal quandles in these rings. Understanding of idempotents is further applied to determine automorphism groups of these quandle rings. Also, commutator width of quandle rings is introduced and computed in a few cases.
Acknowledgments
Bardakov is supported by the Ministry of Science and Higher Education of Russia (agreement No. 075-02-2021-1392). Passi is thankful to Ashoka University, Sonipat, for making their facilities available. Singh acknowledges support from the grants DST/SJF/MSA-02/2018-19 and and SB/SJF/2019-20/04.
Citation
Valeriy G. Bardakov. Inder Bir S. Passi. Mahender Singh. "Zero-divisors and idempotents in quandle rings." Osaka J. Math. 59 (3) 611 - 637, July 2022.
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