Dr. Karl Schwede, Thesis Supervisor Sergei Tabachnikov, Thesis Honors Advisor
Keywords:
Chinese Remainder Theorem Rings Commutative Algebra
Abstract:
This paper studies the geometry of Chinese Remainder Theorem using Hilbert's Nullstellensatz. In the following, I will discuss the background of Chinese Remainder Theorem and give basic definitions for the terms in abstract algebra that we are going to use in this paper. Then, I will present the Chinese Remainder Theorem and its generalization in rings. In addition, I will present the Hilbert's Nullstellensatz and use that to interpret the Chinese Remainder Theorem. Finally, I will change some conditions in Chinese Remainder Theorem and discuss whether it still works.
