Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a generalization of test ideals   The test ideal $\tau(R)$ of a ring $R$ of prime characteristic is an
important object in the theory of tight closure. In this paper, we study a
generalization of the test ideal, which is the ideal $\tau(\a^t)$ associated to
a given ideal $\a$ with rational exponent $t \ge 0$. We first prove a key lemma
of this paper, which gives a characterization of the ideal $\tau(\a^t)$. As
applications of this key lemma, we generalize the preceding results on the
behavior of the test ideal $\tau(R)$. Moreover, we prove an analog of so-called
Skoda's theorem, which is formulated algebraically via adjoint ideals by Lipman
in his proof of the "modified Brian\c{c}on--Skoda theorem."

7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom