Lie and Jordan structures of differentially semiprime rings

Abstract

Properties of Lie and Jordan rings (denoted respectively by \(R^L\) and \(R^J\)) associated with an associative ring \(R\) are discussed. Results on connections between the differentially simplicity (respectively primeness, semiprimeness) of \(R\), \(R^L\) and \(R^J\) are obtained.