Restricted Boolean group rings

Dinesh Udar, R.K. Sharma, and J.B. Srivastava

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