Polynomial rings and the Hilbert Nullstellensatz
McDonald, Arthur Knight
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The purpose of this thesis was to examine the Hilbert Nullstellensatz and some of its more important corollaries. We approached the problem, working primarily with varieties and ideals. The major result is that the ideal associated with the variety of any ideal is the radical of that ideal. Definitions of the terms may be found in the text. It was necessary to develop considerable machinery in order to accomplish the proof. The preliminary details are done at a leisurely pace, with some propositions brought in for their own interest, rather than any application to our future proof. Propositions, which we consider only tools, will be labelled lemmas. Propositions, which are particularly important as independent results, are labelled theorems. Every effort was made to have the paper itself contained, although some experience with field extensions and polynomial rings is presupposed.
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