Jordan regular units in rings and group rings

Keywords: JORDAN REGULAR UNITS

Abstract

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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Published
11.04.2023
How to Cite
KumariP., SahaiM., and SharmaR. K. “Jordan Regular Units in Rings and Group Rings”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 3, Apr. 2023, pp. 351 -63, doi:10.37863/umzh.v75i3.1130.
Section
Research articles