Address: Department of Mathematics, Indian Institute of Technology, Delhi, India
E-mail:
dineshudar@yahoo.com
rksharmaiitd@gmail.com
jbsrivas@gmail.com
Abstract: In this paper we study restricted Boolean rings and group rings. A ring $R$ is $\textit{restricted Boolean}$ if every proper homomorphic image of $R$ is boolean. Our main aim is to characterize restricted Boolean group rings. A complete characterization of non-prime restricted Boolean group rings has been obtained. Also in case of prime group rings necessary conditions have been obtained for a group ring to be restricted Boolean. A counterexample is given to show that these conditions are not sufficient.
AMSclassification: primary 16S34; secondary 20C05, 20C07.
Keywords: group rings, restricted Boolean rings, Boolean rings, neat rings, prime group rings.
DOI: 10.5817/AM2017-3-155