The Grobner ring conjecture in one variable

被引：15

作者：

Lombardi, Henri ^{[1
]}

Schuster, Peter ^{[2
]}

Yengui, Ihsen ^{[3
]}

机构：

[1] Univ Franche Comte, UFR Sci & Tech, UMR CNRS 6623, Equipe Math, F-25030 Besancon, France

[2] Univ Leeds, Leeds LS2 9JT, W Yorkshire, England

[3] Univ Sfax, Fac Sci Sfax, Dept Math, Sfax 3038, Tunisia

来源：

MATHEMATISCHE ZEITSCHRIFT | 2012年 / 270卷 / 3-4期

关键词：

Bezout domain; Valuation domain; Semihereditary ring; Grobner ring conjecture; Constructive mathematics;

D O I：

10.1007/s00209-011-0847-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that a valuation domain V has Krull dimension a parts per thousand currency sign 1 if and only if for every finitely generated ideal I of V[X] the ideal generated by the leading terms of elements of I is also finitely generated. This proves the Grobner ring conjecture in one variable. The proof we give is both simple and constructive. The same result is valid for semihereditary rings.

引用

页码：1181 / 1185

页数：5

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