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| 研究生： |
黃纓茹 Huang Ying-ru |
|---|---|
| 論文名稱： |
有限 Cohen-Macaulay Type 環上的Hilbert-Kunz 函數 On Hilbert-Kunz Function of the Rings of Finite Cohen-Macaulay Type |
| 指導教授： |
洪有情
Hung, Yu-Ching |
| 學位類別： |
碩士 Master |
| 系所名稱： |
數學系 Department of Mathematics |
| 畢業學年度： | 87 |
| 語文別： | 英文 |
| 論文頁數： | 33 |
| 中文關鍵詞： | Hilbert-Kunz 函數 、Frobenius 函子 、有限Cohen-Macaulay type 、諾得局部環 、冪級數 |
| 英文關鍵詞： | Hilbert-Kunz function, Frobenius functor, finite Cohen-Macaulay type, Noetherian local ring, formal power series |
| 論文種類： | 學術論文 |
| 相關次數： | 點閱：322 下載：0 |
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在交換代數中有一個頗有內容的主題"Hilbert Function".在某些特殊的情況下, 藉由討論其冪級數, 我們可以得到一些很好的結果. 取代了討論其生硬的原始定義, 這些很好的結果讓我們能更準確的計算出一些數值, 進而去探討其性質. 延續了"Hilbert Function"的精神與方法,Kunz 致力於探討特徵數為一質數p的諾得局部環, 而他所討論的函數即是所謂的"Hilbert-Kunz Function". 在這裡, 我們將討論有限Cohen-Macaulay
type環的Hilbert-Kunz function, 即 HK(n)=cp^nd+O(p^(d-1)n), 其中c為一實數. 藉由探討其冪級數, 我們能證明c事實上是一個有理數.
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