期刊論文
學年 | 92 |
---|---|
學期 | 1 |
出版(發表)日期 | 2004-01-01 |
作品名稱 | Noether's problem for dihedral 2-groups |
作品名稱(其他語言) | |
著者 | Chu, Huah; Hu, Shou-jen; Kang, Ming-chang |
單位 | 淡江大學數學學系 |
出版者 | Zurich: European Mathematical Society |
著錄名稱、卷期、頁數 | Commentarii Mathematici Helvetici 79(1), pp.147-159 |
摘要 | Let K be any field and G be a finite group. Let G act on the rational function field K(xg:g∈G) by K-automorphisms defined by g⋅xh=xgh for any g,h∈G. Denote by K(G) the fixed field K(xg:g∈G)G. Noethers problem asks whether K(G) is rational (= purely transcendental) over K. We shall prove that K(G) is rational over K if G is the dihedral group (resp. quasi-dihedral group, modular group) of order 16. Our result will imply the existence of the generic Galois extension and the existence of the generic polynomial of the corresponding group. |
關鍵字 | Rationality; Noether's problem; generic Galois extension; generic polynomials; dihedral groups |
語言 | en |
ISSN | 0010-2571 1420-8946 |
期刊性質 | 國外 |
收錄於 | SCI |
產學合作 | |
通訊作者 | |
審稿制度 | |
國別 | CHE |
公開徵稿 | |
出版型式 | 紙本 |
相關連結 |
機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/41693 ) |