{"id":{"repo_id":"dialnet","oai_identifier":"oai:dialnet.unirioja.es:TES0000001212"},"canonical_url":"https://search.dev.ndltd.org/etd/dialnet/oai:dialnet.unirioja.es:TES0000001212","repository":{"repo_id":"dialnet","name":"Dialnet","base_url":"https://dialnet.unirioja.es/oaites/OAIHandler"},"display":{"title":"Combinatorial Koszul Homology: computations and Applications","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Sáenz de Cabezón Irigaray, Eduardo"],"institution":"Universidad de La Rioja (España)","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Hernández Paricio, Luis Javier (Universidad de La Rioja)","Seiler, Werner M. (Universität Mannheim)"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2008,"date_issued":"2008","date_published":"2008","updated_at":"2026-07-24T06:26:37Z","subjects":["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"],"languages":["eng"],"rights":["LICENCIA DE USO: Los documentos a texto completo incluidos en Dialnet son de acceso libre y propiedad de sus autores y/o editores. Por tanto, cualquier acto de reproducción, distribución, comunicación pública y/o transformación total o parcial requiere el consentimiento expreso y escrito de aquéllos. Cualquier enlace al texto completo de estos documentos deberá hacerse a través de la URL oficial de éstos en Dialnet. Más información: https://dialnet.unirioja.es/info/derechosOAI | INTELLECTUAL PROPERTY RIGHTS STATEMENT: Full text documents hosted by Dialnet are protected by copyright and/or related rights. This digital object is accessible without charge, but its use is subject to the licensing conditions set by its authors or editors. Unless expressly stated otherwise in the licensing conditions, you are free to linking, browsing, printing and making a copy for your own personal purposes. All other acts of reproduction and communication to the public are subject to the licensing conditions expressed by editors and authors and require consent from them. Any link to this document should be made using its official URL in Dialnet. More info: https://dialnet.unirioja.es/info/derechosOAI"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dialnet.unirioja.es/servlet/oaites?codigo=13745","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hernández Paricio, Luis Javier (Universidad de La Rioja)","Seiler, Werner M. 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Por tanto, cualquier acto de reproducción, distribución, comunicación pública y/o transformación total o parcial requiere el consentimiento expreso y escrito de aquéllos. Cualquier enlace al texto completo de estos documentos deberá hacerse a través de la URL oficial de éstos en Dialnet. Más información: https://dialnet.unirioja.es/info/derechosOAI | INTELLECTUAL PROPERTY RIGHTS STATEMENT: Full text documents hosted by Dialnet are protected by copyright and/or related rights. This digital object is accessible without charge, but its use is subject to the licensing conditions set by its authors or editors. Unless expressly stated otherwise in the licensing conditions, you are free to linking, browsing, printing and making a copy for your own personal purposes. All other acts of reproduction and communication to the public are subject to the licensing conditions expressed by editors and authors and require consent from them. Any link to this document should be made using its official URL in Dialnet. More info: https://dialnet.unirioja.es/info/derechosOAI"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://dialnet.unirioja.es/servlet/oaites?codigo=13745"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","Esta tesis está centrada en cálculos explícitos y aplicaciones de la homología de Koszul y los números de Betti de ideales monomiales. Con este interés presente, los objetivos principales son: - Analizar la homología de Koszul de ideales monomiales y aplicarla a la descripción de la estructura de dichos ideales. - Describir algoritmos para realizar cálculos eficaces de los invariantes homológicos de ideales de monomios, en particular en números de Betti, resoluciones libres, homología de Koszul y serie de Hilbert. - Aplicar la teoría de ideales monomiales a problemas dentro y fuera de las matemáticas, haciendo uso, en particular, de los invariantes homológicos de estos ideales."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Combinatorial Koszul Homology: computations and Applications"]}]}],"canonical_facts":{"dc:contributor":["Hernández Paricio, Luis Javier (Universidad de La Rioja)","Seiler, Werner M. (Universität Mannheim)"],"dc:creator":["Sáenz de Cabezón Irigaray, Eduardo"],"dc:date":["2008"],"dc:description":["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.","Esta tesis está centrada en cálculos explícitos y aplicaciones de la homología de Koszul y los números de Betti de ideales monomiales. Con este interés presente, los objetivos principales son: - Analizar la homología de Koszul de ideales monomiales y aplicarla a la descripción de la estructura de dichos ideales. - Describir algoritmos para realizar cálculos eficaces de los invariantes homológicos de ideales de monomios, en particular en números de Betti, resoluciones libres, homología de Koszul y serie de Hilbert. - Aplicar la teoría de ideales monomiales a problemas dentro y fuera de las matemáticas, haciendo uso, en particular, de los invariantes homológicos de estos ideales."],"dc:format":["application/pdf"],"dc:identifier":["https://dialnet.unirioja.es/servlet/oaites?codigo=13745"],"dc:language":["eng"],"dc:publisher":["Universidad de La Rioja (España)"],"dc:rights":["LICENCIA DE USO: Los documentos a texto completo incluidos en Dialnet son de acceso libre y propiedad de sus autores y/o editores. Por tanto, cualquier acto de reproducción, distribución, comunicación pública y/o transformación total o parcial requiere el consentimiento expreso y escrito de aquéllos. Cualquier enlace al texto completo de estos documentos deberá hacerse a través de la URL oficial de éstos en Dialnet. Más información: https://dialnet.unirioja.es/info/derechosOAI | INTELLECTUAL PROPERTY RIGHTS STATEMENT: Full text documents hosted by Dialnet are protected by copyright and/or related rights. This digital object is accessible without charge, but its use is subject to the licensing conditions set by its authors or editors. Unless expressly stated otherwise in the licensing conditions, you are free to linking, browsing, printing and making a copy for your own personal purposes. All other acts of reproduction and communication to the public are subject to the licensing conditions expressed by editors and authors and require consent from them. Any link to this document should be made using its official URL in Dialnet. More info: https://dialnet.unirioja.es/info/derechosOAI"],"dc:subject":["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"],"dc:title":["Combinatorial Koszul Homology: computations and Applications"],"dc:type":["text (thesis)"]},"updated_at":"2026-07-24T06:26:37Z"}