指導教授：朱樺臺灣大學：數學研究所王乙珊Wang, Yi-ShanYi-ShanWang2014-11-302018-06-282014-11-302018-06-282014http://ntur.lib.ntu.edu.tw//handle/246246/264005本論文著眼於形式如 ((xn,yn) : Fk) 的零維 Gorenstein 理想,其中 Fk 是在 K[x,y] 中的一個次數為 k 的齊次多項式,K 為代數封閉體。首先,在 k ≤ n 且 Fk 中 xk 的係數 c0 不為 0 的情況下,我們給出一個齊次多項式屬於 ((xn, yn) : Fk) 的充要條件。接下來,我們說明在此情形下 ((xn, yn) : Fk) 可以由二個元素生成。 然後將結果推廣到任意的 c0 與 k。最後,我們介紹 Genoway,Ortiz-Albino 與 Tavares [8] 文章中的一些引理並改寫證明,再加上一個三變數的例子。In this thesis, we are interested in zero-dimensional Gorenstein ideals of the form ((xn,yn) : Fk) where Fk is a homogeneous polynomial of degree k in K[x,y], K an algebraically closed field. Firstly, we figure out the necessary and sufficient condition for a homogenous polynomial to be in ((xn,yn) : Fk) where k ≤ n and the coefficient of xk, denoted by c0, is nonzero. Next, we declare that in this case ((xn,yn) : Fk) can be generated by two elements. Then expand the result to ar- bitrary c0 and k. At last, we introduce some lemmas from the work of Genoway, Ortiz-Albino, and Tavares [8] along with revised proofs and an example in 3 vari- ables.口試委員會審定書.............................................i Acknowledgements.........................................ii Abstract (in Chinese)...................................iii Abstract (in English)....................................iv §0. Introduction..........................................1 §1. Some Lemmas...........................................6 §2. Cases with c0 ̸=0 and k≤n.............................14 §3. Cases with c0 =0 and k≤n.............................30 §4. Discussion...........................................33 References...............................................385554379 bytesapplication/pdf論文公開時間：2014/07/29論文使用權限：同意無償授權Gorenstein 理想生成元thesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/264005/1/ntu-103-R00221018-1.pdf