Radically principal rings

Abstract

Let $A$ be a commutative ring. An ideal $I$ of $A$ is radically principal if there exists a principal ideal $J$ of $A$ such that $sqrt{I}=sqrt{J}$. The ring $A$ is radically principal if every ideal of $A$ is radically principal. In this article, we study radically principal rings. We prove an analogue of the Cohen theorem, precisely, a ring is radically principal if and only if every prime ideal is radically principal. Also we characterize a zero-dimensional radically principal ring. Finally we give a characterization of polynomial ring to be radically principal.