Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cohen-Macaulay, Gorenstein, Complete intersection and regular defect for
  the tensor product of algebras   This paper main goal is to measure the defect of Cohen-Macaulayness,
Gorensteiness, complete intersection and regularity for the tensor product of
algebras over a ring. For this sake, we determine the homological invariants
which are inherent to these notions, such as the Krull dimension, depth,
injective dimension, type and embedding dimension of the tensor product
constructions in terms of those of their components.

34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: nlin