A zero-dimensional valuation ring is 1-Grobner

作者：Li, Dongmei; Liu, Jinwang^*; Zheng, Licui

来源：Journal of Algebra, 2017, 484: 334-343.

DOI：10.1016/j.jalgebra.2017.04.015

• 1-Grobner ring
• Archimedean conjecture
• Grobner ring
• Grobner ring conjecture
• Zero-dimensional valuation ring

In this study, we consider the following conjecture and open problem: (1) A valuation ring R is 1-Grobner if and only if R is an Archimedean ring; (2) Is a 1-Grobner valuation ring coherent? First, we prove that a zero-dimensional valuation ring is 1-Grobner. Furthermore, we give a positive answer to (1) and a negative answer to (2). Finally, we present an example of a valuation ring that is 1-Grobner but not coherent or Noetherian.

• 出版日期2017-8-15
• 单位信息安全国家重点实验室; 湖南科技大学; 中国科学院信息工程研究所