Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Characterization of locally quasi-unmixed rings   Let $\bar{I}$ denote the integral closure of an ideal in a Noetherian ring
$R$. The main result of this paper asserts that $R$ is locally quasi-unmixed if
and only if, the topologies defined by $\overline{I^n}$ and $I^{\langle
n\rangle}$, $\ n\geq 1$, are equivalent. In addition, some results about the
behavior of linearly equivalent topologies of ideals under various ring
homomorphisms are included.

36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys