Weak annihilator over extension rings. (Q411986)

Assume that \(R\) is an associative ring with identity and \(\text{nil}\) is the set of all nilpotent elements of \(R\). For a nonempty subset \(X\) of a ring \(R\), the authors define \(N_R(X)=\{a\in R\mid xa\in\text{nil}\) for all \(x\in X\}\), which is called the weak annihilator of \(X\) in \(R\). In this paper, the authors mainly investigate the properties of the weak annihilator over extension rings.