On rings whose prime ideals are completely prime
For a ring \(R\), the prime radical and the set of all nilpotent elements are denoted by \(P(R)\) and \(N(R)\). A proper two-sided ideal \(I\) of a ring \(R\) is called 2-primal if \(P(R/I)=N(R/I)\). A ring \(R\) is called strongly 2-primal if every proper two-sided ideal of \(R\) is 2-primal. Strongly 2-primal rings with several kinds of \(\pi\)-regularities are studied.
scientific article; zbMATH DE number 1758362