Valuative dimension and monomial orders

JOURNAL OF ALGEBRA

卷:557

Article

Kemper, Gregor¹  Yengui, Ihsen² 

[1] Tech Univ Munich, Zentrum Math M11, Boltzmannstr 3, Garching 85748, Germany

[2] Univ Sfax, Fac Sci Sfax, Dept Math, Sfax 3000, Tunisia

关键词: Krull dimension;    Valuative dimension;    Monomial order;    Non-Noetherian ring;   

DOI  :  10.1016/j.jalgebra.2020.04.017

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free