Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Note on Co-Maximal Ideal Graph of Commutative Rings   Let $R$ be a commutative ring with unity. The co-maximal ideal graph of $R$,
denoted by $\Gamma(R)$, is a graph whose vertices are the proper ideals of $R$
which are not contained in the Jacobson radical of $R$, and two vertices $I_1$
and $I_2$ are adjacent if and only if $I_1 + I_2 = R$. We classify all
commutative rings whose co-maximal ideal graphs are planar. In 2012 the
following question was posed: If $\Gamma(R)$ is an infinite star graph, can $R$
be isomorphic to the direct product of a field and a local ring? In this paper,
we give an affirmative answer to this question.

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The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
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The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph