朱樺臺灣大學:數學研究所石勝吉SHENG - CHI, SHIHSHIHSHENG - CHI2010-05-052018-06-282010-05-052018-06-282008U0001-1507200800501600http://ntur.lib.ntu.edu.tw//handle/246246/180553在第三節中,我們給了兩個比較基本的零點定理的証明。在第四節中,我們討論了不同形式的零點定理的相互關係, 且我們也給了一些不同形式的零點定理的不同的証明。 Alon 是組合的零點定理的主創者, 個定理可以可以用來證明另一個定理 (定理13)並且在組合學和數輪上有很多的應用。 本篇論文中,我們用另外一個觀點來證明此定理並將它推廣(定理12)。在例子 14和例子 15 中,我們也給了一些應用。In Section 4 we give two elementary proofs of Nullstellensatz.The first is due to Enrique Arrondo which is more brief. The second is due to Terrance Tao which is constructive.In Section 5 we will discuss different proofs of above theorems. The first is above three forms which arequivalent. The second we give two different proofs of strong form. The third we give four differentproofs of field form.lon is the principal founder of the Combinatorial Nullstellensatz. This theorem can prove nother theorem (see Theorem 13) which has many applications n combinatorics and number theory. In this paper we will give another view point to this proof and generalize this theorem (see Theorem 12).e also give some applications in Example 14 and Example 15.口試委員會審定書 i bstract in Chinese ii bstract in English iii Introduction 1 Preliminaries on Gr¨obner bases 2 Main theorem 6 Elementary proofs of Nullstellensatz 8 Different forms of Nullstellensatz 15 eferences 21application/pdf276409 bytesapplication/pdfen-US零點定理Grobner 基底組合的零點定理零點定理的証明不同形式的零點定理NullstellensatzCombinatorial NullstellensatzGrobner bases, different forms of Nullstellensatzproofs of Nullstellensatzthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/180553/1/ntu-97-R95221018-1.pdf