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Toric Structure of the Graded Algebra Relative to a Valuation

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Algebra, Arithmetic and Geometry with Applications

Abstract

Throughout this paper, v will denote a valuation of the quotient field F of a Noetherian local domain (R, M). Also, we shall assume that v is centered at R. Denote by K the residue field of R and by S (:= v(R\{0}) the value semigroup of v. For each m ∈ S, set P m (P + m ) := { F ∈ R|v(f ≥ (>) m}). P m and P + m are ideals of R and we call the graded algebra of R relative to v to the S-graded K-algebra

$$ gr_v R = \mathop \oplus \limits_{m \in S} P_m /P_{^m }^ + . $$

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Authors
  1. Antonio Campillo
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  2. Carlos Galindo
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, Northern Kentucky University, Highland Heights, KY, 41099, USA

    Chris Christensen

  2. Department of Mathematics, University of Kentucky, Lexington, KY, 40506, USA

    Avinash Sathaye

  3. Bell Labs, 67, Whippany Road, Whippany, NJ, 07981, USA

    Ganesh Sundaram

  4. Department of Computer Sciences, University of Texas at Austin, Austin, TX, 78712, USA

    Chandrajit Bajaj

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© 2004 Springer-Verlag Berlin Heidelberg

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Campillo, A., Galindo, C. (2004). Toric Structure of the Graded Algebra Relative to a Valuation. In: Christensen, C., Sathaye, A., Sundaram, G., Bajaj, C. (eds) Algebra, Arithmetic and Geometry with Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18487-1_12

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  • DOI: https://doi.org/10.1007/978-3-642-18487-1_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00475-2

  • Online ISBN: 978-3-642-18487-1

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