Commutative algebra finds its roots in invariant theory and the connection is drawn from a modern standpoint. The Hilbert Basis Theorem and the Nullstellenstatz were considered lemmas for classical invariant theory. The Groebner basis is a modern tool used and is implemented with the computer algebra system Mathematica. Number 14 of Hilbert\'s 23 problems is discussed along with the notion of invariance under a group action of GLn(C). Computational difficulties are also discussed in reference to Groebner bases and Invariant theory.The straitening law is presented from a Groebner basis point of view and is motivated as being a key piece of machinery in proving First Fundamental Theorem of Invariant Theory. / Master of Science
Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/23154 |
Date | 05 June 2013 |
Creators | Shifler, Ryan M. |
Contributors | Mathematics, Brown, Ezra A., Green, Edward L., Ball, Joseph A. |
Publisher | Virginia Tech |
Source Sets | Virginia Tech Theses and Dissertation |
Detected Language | English |
Type | Thesis |
Format | ETD, application/pdf |
Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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