Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Closure-interior duality over complete local rings   We define a duality operation connecting closure operations, interior
operations, and test ideals, and describe how the duality acts on common
constructions such as trace, torsion, tight and integral closures, and
divisible submodules. This generalizes the relationship between tight closure
and tight interior given in [Epstein-Schwede 2014] and allows us to extend
commonly used results on tight closure test ideals to operations such as those
above.

31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga