On weak \(\pi\)-regularity of rings whose prime ideals are maximal
A ring \(R\) is 2-primal if the prime radical is the set of all nilpotent elements of \(R\). \(R\) is weakly \(\pi\)-regular if for each \(x\in R\), there exists a natural number \(n\), depending on \(x\), such that \(x^n\in(x^nRx^nR)\cap(Rx^nRx^n)\). The authors investigate the connections between the weak \(\pi\)-regularity and the maximality of prime ideals in 2-primal rings, right quasi-duo rings and PI-rings, respectively, (\(R\) is right quasi-duo if every maximal right ideal of \(R\) is two-sided).
scientific article; zbMATH DE number 1398846