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arXiv · 1906.12067

Valuative dimension and monomial orders

Gregor Kemper·Ihsen Yengui
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Abstract

The main result from this note provides a constructive characterization of the valuative dimension, which bears a strong analogy to Lombardi's 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.

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Gregor Kemper, Ihsen Yengui. 2019-06-28. Valuative dimension and monomial orders. https://arxiv.org/abs/1906.12067

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