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 bas...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.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11871207and 11971161。
文摘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.
