Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability in graded rings associated with commutative augmented rings   Let $A$ be a commutative augmented ring and $I$ be its augmentation ideal.
This paper shows that the sequence $\{I^n/I^{n+1}\}$ becomes stationary up to
isomorphism. The result yields stability in the associated graded ring of $A$
along $I$.

16
The categories of this paper are: stat
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga