In this paper, we prove the main result: Let both (K, S) and (K*, S*) be preordered fields, and let (K*, S*) be a finitely generated extension of (K, S). If K* is transcendental over K, then (K*, S*) has the weak Hilb...In this paper, we prove the main result: Let both (K, S) and (K*, S*) be preordered fields, and let (K*, S*) be a finitely generated extension of (K, S). If K* is transcendental over K, then (K*, S*) has the weak Hilbert property. This result answers negatively an open problem posed by the author in reference[1]. Moreover, some results on the weak Hilbert property are established. In this paper, we prove the main result: Let both (K, S) and (K*, S*) be preordered fields, and let (K*, S*) be a finitely generated extension of (K, S). If K* is transcendental over K, then (K*, S*) has the weak Hilbert property. This result answers negatively an open problem posed by the author in reference [1]. Moreover, some results on the weak Hilbert property are established.展开更多
In this paper, we give the definition of the height of a valuation and the definition of the big field ? p,G , where p is a prime and G ? ? is an additive subgroup containing 1. We conclude that ? p,G is a field and ?...In this paper, we give the definition of the height of a valuation and the definition of the big field ? p,G , where p is a prime and G ? ? is an additive subgroup containing 1. We conclude that ? p,G is a field and ? p,G is algebraically closed. Based on this the author obtains the complete classification of valuations on arithmetic surfaces. Furthermore, for any m ? p,G n ∈ ?, let V m,n be an ∝-vector space of dimension n - m + 1, whose coordinates are indexed from m to n. We generalize the definition of ? p,G , where p is a prime and G ? V m,n is an additive subgroup containing 1. We also conclude that ? p,G is a field if m ? 0 ? n.展开更多
基金Project supported by National Natural Science Foundation of China
文摘In this paper, we prove the main result: Let both (K, S) and (K*, S*) be preordered fields, and let (K*, S*) be a finitely generated extension of (K, S). If K* is transcendental over K, then (K*, S*) has the weak Hilbert property. This result answers negatively an open problem posed by the author in reference[1]. Moreover, some results on the weak Hilbert property are established. In this paper, we prove the main result: Let both (K, S) and (K*, S*) be preordered fields, and let (K*, S*) be a finitely generated extension of (K, S). If K* is transcendental over K, then (K*, S*) has the weak Hilbert property. This result answers negatively an open problem posed by the author in reference [1]. Moreover, some results on the weak Hilbert property are established.
文摘In this paper, we give the definition of the height of a valuation and the definition of the big field ? p,G , where p is a prime and G ? ? is an additive subgroup containing 1. We conclude that ? p,G is a field and ? p,G is algebraically closed. Based on this the author obtains the complete classification of valuations on arithmetic surfaces. Furthermore, for any m ? p,G n ∈ ?, let V m,n be an ∝-vector space of dimension n - m + 1, whose coordinates are indexed from m to n. We generalize the definition of ? p,G , where p is a prime and G ? V m,n is an additive subgroup containing 1. We also conclude that ? p,G is a field if m ? 0 ? n.
