Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The tiny trace ideals of the canonical modules in Cohen-Macaulay rings
  of dimension one   We study one-dimensional Cohen-Macaulay rings whose trace ideal of the
canonical module is as small as possible. In this paper we call such rings
far-flung Gorenstein rings. We investigate far-flung Gorenstein rings in
relation with the endomorphism algebras of the maximal ideals and numerical
semigroup rings. We show that the solution of the Rohrbach problem in additive
number theory provides an upper bound for the multiplicity of far-flung
Gorenstein numerical semigroup rings. Reflexive modules over far-flung
Gorenstein rings are also studied.

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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: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci