Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Graded Radically Principal Ideals   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 $R[X]$.

11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: stat
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: eess