Jordan regular units in rings and group rings - Kumari, P.; Sahai, M.; Sharma, R. K. (Ukrains’kyi Matematychnyi Zhurnal, 2023)
UDC 512.5 The concept of Lie regular elements and Lie regular units was defined and studied by Kanwar, Sharma and Yadav in Lie regular generators of general linear groups, Comm. Algebra, 40, № 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(2, Z_2^n) is equal to a half of the order of U(M(2,Z_2^n)). Further, we show that the group ring KG of a group G over a field K of characteristic 2 has no Jordan regular units.