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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.","abstract_html":"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.","abstract_has_math":false,"creators":["Shifler, Ryan M."],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Brown, Ezra A."],"committee_members":["Green, Edward L.","Ball, Joseph A."],"year":2013,"date_issued":"2013-06-05","date_published":"2013-06-05","updated_at":"2026-07-22T22:20:43Z","subjects":["Groebner Basis","Invariant Theory","Algorithm"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:810"],"render_values":[{"text":"vt_gsexam:810","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/23154","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Brown, Ezra A."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Green, Edward L.","Ball, Joseph A."]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Shifler, Ryan M."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2013-06-06T08:00:42Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2013-06-06T08:00:42Z"]},{"key":"dc:date.issued","label":"Date","values":["2013-06-05"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Groebner Basis","Invariant Theory","Algorithm"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:810"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/23154"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Commutative algebra finds its roots in invariant theory and the connection is drawn from a modern standpoint. 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