J-Boolean group rings and skew group rings

摘要

A ring R is called semiboolean if R/J(R) is boolean and idempotents lift modulo J(R), where J(R) denotes the Jacobson radical of R. In this paper, we define J-boolean rings as a generalization of semiboolean rings. A ring R is said to be ,J-boolean if R/J(R) is boolean. Various basic properties of these rings are obtained. The J-boolean group rings and skew group rings have been studied. It is investigated whether the results obtained for J-boolean group rings also hold for the skew group rings.