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1	Computational Algebraic Geometry Applied to Invariant Theory Shifler, Ryan M. 05 June 2013 (has links) 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 Groebner Basis Invariant Theory Algorithm
2	Groebner Finite Path Algebras Leamer, Micah J. 15 July 2004 (has links) Let K be a field and Q a finite directed multi-graph. In this paper I classify all path algebras KQ and admissible orders with the property that all of their finitely generated ideals have finite Groebner bases. / Master of Science Path Algebra Groebner Basis Groebner Bases
3	Algebraic Methods for Proving Geometric Theorems Redman, Lynn 01 September 2019 (has links) Algebraic geometry is the study of systems of polynomial equations in one or more variables. Thinking of polynomials as functions reveals a close connection between affine varieties, which are geometric structures, and ideals, which are algebraic objects. An affine variety is a collection of tuples that represents the solutions to a system of equations. An ideal is a special subset of a ring and is what provides the tools to prove geometric theorems algebraically. In this thesis, we establish that a variety depends on the ideal generated by its defining equations. The ability to change the basis of an ideal without changing the variety is a powerful tool in determining a variety. In general, the quotient and remainder on division of polynomials in more than one variable are not unique. One property of a Groebner basis is that it yields a unique remainder on division. To prove geometric theorems algebraically, we first express the hypotheses and conclusions as polynomials. Then, with the aid of a computer, apply the Groebner Basis Algorithm to determine if the conclusion polynomial(s) vanish on the same variety as the hypotheses. affine varieties ideals geometric theorems Groebner basis Algebraic Geometry
4	The Groebner basis of a polynomial system related to the Jacobian conjecture / The Groebner basis of a polynomial system related to the Jacobian conjecture Valqui Haase, Christian Holger, Solórzano, Marco 25 September 2017 (has links) We compute the Groebner basis of a system of polynomial equations related to the Jacobian conjecture using a recursive formula for the Catalan numbers. / En este artículo calculamos la base de Groebner de un sistema polinomial de ecuaciones relacionada con la conjetura del jacobiano utilizando una fórmula recursiva para los numeros de Catalan. Jacobian Groebner Basis Catalan Numbers 14r15 13f20 11b99 Jacobiano Bases de Groebner Números de Catalan 14r15 13f20 11b99
5	Poincaredualitätsalgebren, Koinvarianten und Wu-Klassen / Poincare Duality Algebras, Coinvariants and Wu Classes Kuhnigk, Kathrin 22 May 2003 (has links) No description available. 510 Mathematik Mathematics and Computer Science Poincaredualität Invariantentheorie Steenrod-Algebra Wu-Klassen Koinvarianten Groebner-Basis Macaulay Poincare Duality Invariant Theory Steenrod Algebra Wu Classes Coinvariants Groebner Basis Macaulay 31.23 31.51 Mathematik zur Zeit nicht erreichbar

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