Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nakayama closures, interior operations, and core-hull duality   Exploiting the interior-closure duality developed by Epstein and R.G., we
show that for the class of Matlis dualizable modules $\mathcal{M}$ over a
Noetherian local ring, when cl is a Nakayama closure and i its dual interior,
there is a duality between cl-reductions and i-expansions that leads to a
duality between the cl-core of modules in $\mathcal{M}$ and the i-hull of
modules in $\mathcal{M}^\vee$. We further show that many algebra and module
closures and interiors are Nakayama and describe a method to compute the
interior of ideals using closures and colons. We use our methods to give a
unified proof of the equivalence of F-rationality with F-regularity, and of
F-injectivity with F-purity, in the complete Gorenstein local case.
Additionally, we give a new characterization of the finitistic tight closure
test ideal in terms of maps from $R^{1/p^e}$. Moreover, we show that the
liftable integral spread of a module exists.

12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
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The categories of this paper are: quant-ph