Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariance of a length associated to a reduction   Let $(A, \mathfrak{m})$ be a $d$-dimensional Cohen-Macaulay local ring with
infinite residue field and let $J$ be a minimal reduction of $\mathfrak{m}$. We
show that $\lambda(\mathfrak{m}^3/J\mathfrak{m}^2)$ is independent of $J$.

27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
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The categories of this paper are: eess
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn