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 ) |