Nonnil-Laskerian rings (Q2094263)

Let \(R\) be a commutative ring with unity and \(\mathrm{Nil}(R)\) its nilradical; i.e, the set of its nilpotent elements. An ideal \(I\) of \(R\) is said decomposable if it is an intersection of finite number of primary ideals. It is nonnil if \(I\not\subseteq\mathrm{Nil}(R)\). The ring \(R\) is said nonnil-Laskerian if each nonnil ideal is decomposable. In this paper, the author show that the concepts of Laskerian and nonnil-Laskerian rings are different but they share many interesting properties. However, they differ when we consider the polynomial and the power series extensions.