Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some Remarks on $\phi$-Dedekind rings and $\phi$-Prufer rings   In this paper, the notions of nonnil-injective modules and
nonnil-FP-injective modules are introduced and studied. Especially, we show
that a $\phi$-ring $R$ is an integral domain if and only if any
nonnil-injective (resp., nonnil-FP-injective) module $R$-module is injective
(resp., FP-injective). Some new characterizations of $\phi$-von Neumann regular
rings, nonnil-Notherian rings and nonnil-coherent rings are given. We finally
characterize $\phi$-Dedekind rings and $\phi$-\Prufer\ rings in terms of
$\phi$-flat modules, nonnil-injective modules and nonnil-FP-injective modules.

22
The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
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The categories of this paper are: solv-int