Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ideals defining Gorenstein rings are (almost) never products   This note proves that if S is an unramified regular local ring and I and J
are proper ideals of height at least two, then S/IJ is never Gorenstein.

32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an