On Nullstellensatz

• Main Authors: SHENG - CHI, SHIH, 石勝吉
• Other Authors: 朱樺
• Format: Others
• Language: en_US
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/78253842934223288141

碩士 === 國立臺灣大學 === 數學研究所 === 96 === 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 are equivalent. The second we give two different proofs of strong form. The third we give four differentproofs of field form. Alon is the principal founder of the Combinatorial Nullstellensatz. This theorem can prove another theorem (see Theorem 13) which has many applications in combinatorics and number theory. In this paper we will give another view point to this proof and generalize this theorem (see Theorem 12). We also give some applications in Example 14 and Example 15.