Combinatorial Koszul Homology: computations and Applications

With a particular focus on explicit computations and applications of the Koszul homology and Betti numbers of monomial ideals, the main goals od this thesis are the following: Analyze the Koszul homology of monomial ideals and apply it to describe the structure of monomial ideals. Describe algorithms to perform efficient computations of the homological invariants of monomial ideals. Apply the theory and computations on monomial ideals to problems inside and outside mathematics. The thesis introduces as a main tool Mayer-Vietoris trees of monomial ideals.

Grantor dc:publisher

Universidad de La Rioja (España)

Year dc:date

2008

Author dc:creator

• Sáenz de Cabezón Irigaray, Eduardo

Contributors dc:contributor

• Hernández Paricio, Luis Javier (Universidad de La Rioja)
• Seiler, Werner M. (Universität Mannheim)

• homología de Koszul
• álgebra conmutativa combinatoria
• ideales monomiales
• números de Betti
• análisis algebráico de la fiabilidad de sistemas
• teoría formal de sistemas diferenciales
• Koszul homology
• combinatorial commutative algebra
• monomial ideals
• Betti numbers
• algebraic analysis of system reliability
• formal theory of differential systems

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Language dc:language

eng

Repository record dc:identifier

https://dialnet.unirioja.es/servlet/oaites?codigo=13745

OAI identifier oai:identifier

oai:dialnet.unirioja.es:TES0000001212