Polynomial rings and the Hilbert Nullstellensatz

Thesis (M.A.)--Boston UniversityPLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you.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.2031-01-0