Some notes on semiabelian rings. (Q638069)

Summary: A ring \(R\) is called semiabelian if every idempotent of \(R\) is either right semicentral or left semicentral. It is proved that if a ring \(R\) is semiabelian, then so is the skew polynomial ring \(R[x;\sigma]\), where \(\sigma\) is an endomorphism of \(R\) satisfying \(\sigma(e)=e\) for all \(e\in E(R)\). Some characterizations and properties of semiabelian rings are studied.