Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On ascending chains of ideals in the polynomial ring   Assume that $K$ is a field and $I_{1}\subsetneq ...\subsetneq I_{t}$ is an
ascending chain (of length $t$) of ideals in the polynomial ring
$K[x_{1},,...,x_{m}]$, for some $m\geq 1$. Suppose that $I_{j}$ is generated by
polynomials of degrees less or equal to some natural number $f(j)\geq 1$, for
any $j=1,...,t$. In the paper we construct, in an elementary way, a natural
number $\mathcal{B}(m,f)$ (depending on $m$ and the function $f$) such that
$t\leq\mathcal{B}(m,f)$. We also discuss some possible applications of this
result.

24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc