Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Small Injective Rings   Let $R$ be a ring, a right ideal $I$ of $R$ is called small if for every
proper right ideal $K$ of $R$, $I+K\neq R$. A ring $R$ is called right small
injective if every homomorphism from a small right ideal to $R_{R}$ can be
extended to an $R$-homomorphism from $R_{R}$ to $R_{R}$. Properties of small
injective rings are explored and several new characterizations are given for
$QF$ rings and $PF$ rings, respectively.

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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: econ