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Restricted Boolean group rings. (English) Zbl 1424.16051
Summary: In this paper we study restricted Boolean rings and group rings. A ring \(R\) is 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 is obtained. Also in case of prime group rings necessary conditions are obtained for a group ring to be restricted Boolean. A counterexample is given to show that these conditions are not sufficient.
MSC:
16S34 Group rings
20C05 Group rings of finite groups and their modules (group-theoretic aspects)
20C07 Group rings of infinite groups and their modules (group-theoretic aspects)
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