Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on the construction of finitely injective modules   We develop a technique to construct finitely injective modules which are non
trivial, in the sense that they are not direct sums of injective modules. As a
consequence, we prove that a ring $R$ is left noetherian if and only if each
finitely injective left $R$-module is trivial, thus answering an open question
posed by Salce.

12
The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: eess
30
The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: econ