A Problem about the Weak Hilbert Property  

作　　者：Zeng Guangxing, Departement of Mathematics and Systems Science, Nanchang University, Nanchang 330047, China 

出　　处：《Acta Mathematica Sinica,English Series》1998年第4期481-486,共6页数学学报（英文版）

基　　金：Project supported by National Natural Science Foundation of China

摘　　要：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.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.

关 键 词：Ordered field Preordered field The weak Hilbert property Positive definite polynomial 

分 类 号：O1[理学—数学]