Jordan regular units in rings and group rings
DOI:
https://doi.org/10.37863/umzh.v75i3.1130Keywords:
JORDAN REGULAR UNITSAbstract
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.
References
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