A Study of Nullstellensatz

Abstract

In this thesis, we introduce Hilbert's Nullstellensatz and give several differ- ent proofs of various forms of the Nullstellensatz. First, we introduce the proof of Hilbert's Nullstellensatz by using the strongest and most general version of Nullstellensatz. We then give intersting proofs of Hilbert's Nullstellensatz for two special cases in which the ground fields satisfy narrower conditions. Finally, we give another proof of Hilbert's Nullstellensatz with the idea used in proving one of the special cases.