Date of Award

Fall 11-15-2012

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Dr. Florian Enescu

Second Advisor

Dr. Frank Hall

Third Advisor

Dr. Yongwei Yao

Abstract

This thesis presents the theory of affine algebraic sets defined over an arbitrary field K. We define basic concepts such as the Zariski topology, coordinate ring of functions, regular functions, and dimension. We are interested in the relationship between the geometry of an affine algebraic set over a field K and its geometry induced by the algebraic closure of K. Various versions of Hilbert-Nullstellensatz are presented, introducing a new variant over finite fields. Examples are provided throughout the paper and a question on the dimension of irreducible affine algebraic sets is formulated.

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