Commun. Korean Math. Soc. 2018; 33(4): 1075-1082
Online first article July 11, 2018 Printed October 31, 2018
https://doi.org/10.4134/CKMS.c170393
Copyright © The Korean Mathematical Society.
Emad Abu Osba, Hasan Al-Ezeh, Manal Ghanem
The University of Jordan, The University of Jordan, The University of Jordan
Let $R$ be a commutative ring, $G$ be an Abelian group, and let $RG$ be the group ring. We say that $RG$ is a U-group ring if $a$ is a unit in $RG$ if and only if $\epsilon (a)$ is a unit in $R$. We show that $RG$ is a U-group ring if and only if $G$ is a p-group and $p\in J(R)$. We give some properties of U-group rings and investigate some properties of well known rings, such as Hermite rings and rings with stable range, in the presence of U-group rings.
Keywords: group ring, Hermite ring, rings with stable range, Jacobson radical, p-group
MSC numbers: 13A99, 16S34, 20C05, 20C07
2020; 35(1): 117-124
2019; 34(1): 127-136
1999; 14(3): 513-519
2002; 17(2): 245-252
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd