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
This paper investigates the completion and the zero prime factorization for matrices over a K-Hermite ring. The authors have generalized Kaplansky's related results, solved similar Lin-Bose problem and generalized...This paper investigates the completion and the zero prime factorization for matrices over a K-Hermite ring. The authors have generalized Kaplansky's related results, solved similar Lin-Bose problem and generalized Serre problem over a K-Hermite ring.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.
基金supported by the National Natural Science Foundation of China under Grant Nos.11501192,11471108,11426101Hunan Provincial Natural Science Foundation under Grant No.2015JJ2051Scientific Research Fund of Hunan Province Education Department under Grant No.15B082
文摘This paper investigates the completion and the zero prime factorization for matrices over a K-Hermite ring. The authors have generalized Kaplansky's related results, solved similar Lin-Bose problem and generalized Serre problem over a K-Hermite ring.
