Bull. Korean Math. Soc. 2023; 60(1): 83-91
Online first article September 1, 2022 Printed January 31, 2023
https://doi.org/10.4134/BKMS.b210917
Copyright © The Korean Mathematical Society.
Kanchan Jangra, Dinesh Udar
Delhi Technological University; Delhi Technological University
A ring $R$ is called a UN ring if every non unit of it can be written as product of a unit and a nilpotent element. We obtain results about lifting of conjugate idempotents and unit regular elements modulo an ideal $I$ of a UN ring $R$. Matrix rings over UN rings are discussed and it is obtained that for a commutative ring $R$, a matrix ring $M_n(R)$ is UN if and only if $R$ is UN. Lastly, UN group rings are investigated and we obtain the conditions on a group $G$ and a field $K$ for the group algebra $KG$ to be UN. Then we extend the results obtained for $KG$ to the group ring $RG$ over a ring $R$ (which may not necessarily be a field).
Keywords: UN rings, units, nilpotents, group rings
MSC numbers: Primary 16N40, 16S34, 16U60, 20C05, 20C07
2023; 60(3): 829-844
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