Radically principal rings

Document Type: Original Article

Authors

1 Sidi Mohamed Ben Abdellah University, Higher Normal school, Fez,

2 Department of Mathematics, Faculty of Sciences and technologies, University Sidi Mohamed Ben Abdallah Fes, Morocco.

10.22034/kjm.2020.109821

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.

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