Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graded AR Sequences and the Huneke-Wiegand Conjecture   We let R be a one-dimensional graded complete intersection, satisfying
certain degree conditions which are satisfied whenever R is a numerical
semigroup ring of embedding dimension at least three. We show that a graded
maximal Cohen-Macaulay R-module M satisfies the Huneke-Wiegand Conjecture
provided there exists an Auslander-Reiten sequence ending in M whose middle
term has at least two nonfree direct summands.

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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th