A Grobner Basis Algorithm for Ideals over Zero-Dimensional Valuation Rings  

作　　者：LI Dongmei LIU Jinwang 

机构地区：[1]College of Mathematics and Computations,Hunan University of Science and Technology,Xiangtan 411201,China

出　　处：《Journal of Systems Science & Complexity》2021年第6期2470-2483,共14页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant Nos.11871207and 11971161。

摘　　要：Zero-dimensional valuation rings are one kind of non-Noetherian rings.This paper investigates properties of zero-dimensional valuation rings and prove that a finitely generated ideal over such a ring has a Grobner basis.The authors present an algorithm for computing a Gr?bner basis of a finitely generated ideal over it.Furthermore,an interesting example is also provided to explain the algorithm.

关 键 词：Non-Noetherian ring Grobner basis Gr?bner ring conjecture valuation ring 

分 类 号：O153.3[理学—数学]