The concept of Lie regular elements and Lie regular units was defined and studied by Kanwar, Sharma, and Yadav in Comm. Algebra, 40, No. 4, 1304–1315 (2012). We introduce Jordan regular elements and Jordan regular units. It is proved that the order of the set of Jordan regular units in \(M\left(2,{Z}_{{2}^{n}}\right)\) is equal to a half of the order of \(U\left(M\left(2,{Z}_{{2}^{n}}\right)\right)\). Further, we show that the group ring KG of a group G over a field K of characteristic 2 has no Jordan regular units.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 3, pp. 351–363, March, 2023. Ukrainian DOI: https://doi.org/10.37863/umzh.v75i3.1130.
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Kumari, P., Sahai, M. & Sharma, R.K. Jordan Regular Units in Rings and Group Rings. Ukr Math J 75, 403–418 (2023). https://doi.org/10.1007/s11253-023-02207-5
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DOI: https://doi.org/10.1007/s11253-023-02207-5