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On the graded algebra relative to a valuation

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Abstract

The graded algebragr v R relative to a valuationv of the quotient field of a noetherian local domainR centered atR is anS-gradedK-algebra whereS is the value semigroup ofv andK the residue field ofR. We show how the semigroup theoretical properties ofS allow to describe a minimal system of homogeneous generators forgr v R and to obtain anS-graded minimal resolution ofgr v R asA[v]-module,A[v] being certain associated polynomial ring. We derive a formula to obtain the number of generators of a fixed degree (inS) for each syzygy module and so to compute them in combinatorial terms.

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Authors and Affiliations

  1. D. Algebra, Fac. de Ciencias, Prado de la Magdalena sn., 47005, Valladolid, Spain

    Antonio Campillo

  2. D. Matemáticas, ESTCE, UJI, Campus P.Roja, 12071, Castellón, Spain

    Carlos Galindo

Authors
  1. Antonio Campillo
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  2. Carlos Galindo
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Campillo, A., Galindo, C. On the graded algebra relative to a valuation. Manuscripta Math 92, 173–189 (1997). https://doi.org/10.1007/BF02678188

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  • DOI: https://doi.org/10.1007/BF02678188

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