Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximal ideals in module categories and applications   We study the existence of maximal ideals in preadditive categories defining
an order $\preceq$ between objects, in such a way that if there do not exist
maximal objects with respect to $\preceq$, then there is no maximal ideal in
the category. In our study, it is sometimes sufficient to restrict our
attention to suitable subcategories. We give an example of a category $\mathbf
C_F$ of modules over a right noetherian ring $R$ in which there is a unique
maximal ideal. The category $\mathbf C_F$ is related to an indecomposable
injective module $F$, and the objects of $\mathbf C_F$ are the $R$-modules of
finite $F$-rank.

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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
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The categories of this paper are: adap-org