Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds for numbers of generators for a class of submodules of a finitely
  generated module   The aim of this paper is to obtain a uniform bound for a certain class of
submodules from the following theorem: Let $(R,\frak m)$ be a local ring, let
$M$ be a finite $R$--module of dimension $d\ge 1$ and let $\frak q$ be an ideal
of $R$ generated by a system of parameters on $M$. Let $N$ be a submodule of
$M$ with $\depth M/N\ge d-1$. Then $\ell(N/\frak qN)\le\ell(M/\frak qM)$.

8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th