Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Small perturbations in generalized Cohen-Macaulay local rings   Let $(R, \frak m)$ be a generalized Cohen-Macaulay local ring of dimension
$d$, and $f_1, \ldots, f_r$ a part of system of parameters of $R$. In this
paper we give explicit numbers $N$ such that the lengths of all lower local
cohomology modules and the Hilbert function of $R/(f_1, \ldots, f_r)$ are
preserved when we perturbs the sequence $f_1, \ldots, f_r$ by $\varepsilon_1,
\ldots, \varepsilon_r \in {\frak m}^N$. The second assertion extends a previous
result of Srinivas and Trivedi for generalized Cohen-Macaulay rings.

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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex