Type of Document Master's Thesis Author Zagrodny, Christopher Michael Author's Email Address czagrodny1@student.gsu.edu URN etd-04232006-185220 Title Algebraic Concepts in the Study of Graphs and Simplicial Complexes Degree Master of Science Department Mathematics and Statistics Advisory Committee
Advisor Name Title Florian Enescu Committee Chair Guantao Chen Committee Member Mihaly Bakonyi Committee Member Keywords
- Commutative Algebra
- Graph Theory
- Stanley-Reisner Rings
Date of Defense 2006-04-06 Availability unrestricted Abstract This paper presents a survey of concepts in commutative algebra thathave applications to topology and graph theory. The primary
algebraic focus will be on Stanley-Reisner rings, classes of
polynomial rings that can describe simplicial complexes.
Stanley-Reisner rings are defined via square-free monomial ideals.
The paper will present many aspects of the theory of these ideals
and discuss how they relate to important constructions in
commutative algebra, such as finite generation of ideals, graded
rings and modules, localization and associated primes, primary
decomposition of ideals and Hilbert series. In particular, the
primary decomposition and Hilbert series for certain types of
monomial ideals will be analyzed through explicit examples of
simplicial complexes and graphs.
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