Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Frobenius maps on injective hulls and their applications to tight
  closure   This paper studies Frobenius maps on injective hulls of residue fields of
complete local rings with a view toward providing constructive descriptions of
objects originating from the theory of tight closure. Specifically, the paper
describes algorithms for computing parameter test ideals, and tight closure of
certain submodules of the injective hull of residue fields of a class of
well-behaved rings which includes all quasi-Gorenstein complete local rings.

13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
16
The categories of this paper are: stat
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci