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
Some equivalent characterizations for a skew group ring to be a Dubrovin valuation ring are given.Among them all the prime ideals of a Dubrovin valuation skew group ring are characterised.
In this paper,the notion of rational univariate representations with variables is introduced.Consequently,the ideals,created by given rational univariate representations with variables,are defined.One merit of these c...In this paper,the notion of rational univariate representations with variables is introduced.Consequently,the ideals,created by given rational univariate representations with variables,are defined.One merit of these created ideals is that some of their algebraic properties can be easily decided.With the aid of the theory of valuations,some related results are established.Based on these results,a new approach is presented for decomposing the radical of a polynomial ideal into an intersection of prime ideals.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 China Natural Science Funds(60075016)Guangxi Natural Science Funds(0135005)Guangxi Selected Experts Funds
文摘Some equivalent characterizations for a skew group ring to be a Dubrovin valuation ring are given.Among them all the prime ideals of a Dubrovin valuation skew group ring are characterised.
基金supported by the National Natural Science Foundation of China under Grant No.12161057。
文摘In this paper,the notion of rational univariate representations with variables is introduced.Consequently,the ideals,created by given rational univariate representations with variables,are defined.One merit of these created ideals is that some of their algebraic properties can be easily decided.With the aid of the theory of valuations,some related results are established.Based on these results,a new approach is presented for decomposing the radical of a polynomial ideal into an intersection of prime ideals.
