Valuative dimension and monomial orders

Gregor Kemper, Ihsen Yengui

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

The main result from this note provides a constructive characterization of the valuative dimension, which bears a strong analogy to Lombardi's [7] constructive characterization of the Krull dimension. While Lombardi's characterization uses the lexicographic monomial order, ours uses the graded (reverse) lexicographic order or, in fact, any graded rational monomial order. Apart from this, the paper contains some related results and some examples which readers may find illuminating.

Original languageEnglish
Pages (from-to)278-288
Number of pages11
JournalJournal of Algebra
Volume557
DOIs
StatePublished - 1 Sep 2020

Keywords

  • Krull dimension
  • Monomial order
  • Non-Noetherian ring
  • Valuative dimension

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