朱樺臺灣大學：數學研究所林泰均Lin, Tai-JiunTai-JiunLin2007-11-282018-06-282007-11-282018-06-282007http://ntur.lib.ntu.edu.tw//handle/246246/59487本論文中，我們算出某些情況下Gorenstein理想的生成元。我們對二項式的情況重給簡潔的証明並討論三項式的某一類情況: x^{ rho}y_{1}^{sigma_{1}}cdots y_{s}^{sigma_{s}} z_{1}^{ tau_{1}}cdots z_{t}^{ tau_{t}}(x^{w}-y_{1}^{u_{1}} cdots y_{s}^{u_{s}}-z_{1}^{v_{1}}cdots z_{t}^{v_{t}}) 。我們只給出生成元的領導項，而整個生成元可以由證明的過程寫出。In this paper, we compute generators of Gorenstein ideals in some special case. We give another proof of the binomial case and discuss a trinomial of the form x^{ rho}y_{1}^{sigma_{1}}cdots y_{s}^{sigma_{s}} z_{1}^{ tau_{1}}cdots z_{t}^{ tau_{t}}(x^{w}-y_{1}^{u_{1}} cdots y_{s}^{u_{s}}-z_{1}^{v_{1}}cdots z_{t}^{v_{t}}) . We just give the leading terms of the generators. And the entire generators can be written out in the process of the proofs.口試委員會審員書…………………………………………………i 誌謝………………………………………………………………… ii 中文摘要………………………………………………………………………iii 英文摘要………………………………………………………………………iv 第一章 Introduction…………………………………………………………1 第二章Preliminary………………………………………………………….3 第三章 Binomials………………………………………………………………5 第四章 Trinomials……………………………………………………………11 參考文獻……………………………………………………………………..47388417 bytesapplication/pdfen-USGorensteinthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/59487/1/ntu-96-R94221028-1.pdf