Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Specialization and Integral Closure   We prove that the integral closedness of any ideal of height at least two is
compatible with specialization by a generic element. This opens the possibility
for proofs using induction on the height of an ideal. Also, with additional
assumptions, we show that an element is integral over a module if it is
integral modulo a generic element of the module. This turns questions about
integral closures of modules into problems about integral closures of ideals,
by means of a construction known as Bourbaki ideal.

9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th