  Let $R$ be a commutative $G$-graded ring with a nonzero unity. In this
article, we introduce the concept of graded radically principal ideals. A
graded ideal $I$ of $R$ is said to be graded radically principal if
$Grad(I)=Grad(\langle c\rangle)$ for some homogeneous $c\in R$, where $Grad(I)$
is the graded radical of $I$. The graded ring $R$ is said to be graded
radically principal if every graded ideal of $R$ is graded radically principal.
We study graded radically principal rings. We prove an analogue of the Cohen
theorem, in the graded case, precisely, a graded ring is graded radically
principal if and only if every graded prime ideal is graded radically
principal. Finally we study the graded radically principal property for the
polynomial ring $R[X]$.
