Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pretty cleanness and filter-regular sequences   Let $K$ be a field and $S=K[x_1,\ldots, x_n]$. Let $I$ be a monomial ideal of
$S$ and $u_1,\ldots, u_r$ be monomials in $S$ which form a filter-regular
sequence on $S/I$. We show that $S/I$ is pretty clean if and only if
$S/(I,u_1,\ldots, u_r)$ is pretty clean.

24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph