Theory of associated and attached prime ideals over quantum algebras
| dc.contributor.advisor | Reyes Villamil, Milton Armando | |
| dc.contributor.author | Higuera Rincón, Sebastián David | |
| dc.contributor.orcid | Higuera Rincón, Sebastián David [0009-0003-4520-2802] | |
| dc.contributor.researchgate | Higuera Rincón, Sebastián David [Sebastian-Higuera-4] | |
| dc.date.accessioned | 2025-09-16T15:01:42Z | |
| dc.date.available | 2025-09-16T15:01:42Z | |
| dc.date.issued | 2024 | |
| dc.description.abstract | En esta tesis estudiamos la propiedad nilpotente-reflexiva (RNP para abreviar) sobre álgebras cuánticas como anillos de polinomios torcidos y extensiones PBW torcidas. Investigamos la transferencia de esta propiedad entre anillos de coeficientes y anillos no conmutativos de tipo polinomial sobre estos anillos. Consideramos esta propiedad para localizaciones mediante elementos regulares de extensiones PBW torcidas. En relación con la propiedad RNP, estudiamos las nociones de anulador débil e ideal primo asociado nilpotente, y formulamos varios resultados que extienden o contribuyen a los correspondientes en la literatura. Adicionalmente, investigamos los ideales primos asociados de módulos inducidos sobre álgebras cuánticas y los caracterizamos. Nuestro trabajo es una contribución a una extensa investigación presentada por diferentes autores sobre las propiedades teóricas de los anillos no conmutativos y su descripción de los ideales primos asociados. Por otro lado, motivados por la investigación sobre los ideales primos adjuntos del módulo polinomial inverso sobre anillos de polinomios torcidos de tipo automorfismo, y considerando una familia muy importante de álgebras cuánticas conocidas como polinomios de Ore torcidos de orden superior, caracterizamos los ideales primos adjuntos de esos módulos sobre polinomios de Ore torcidos. También formulamos resultados sobre la dimensión uniforme y los primos asociados de módulos inducidos sobre algunas familias de álgebras cuánticas. Finalmente, estudiamos la dimensión couniforme para módulos polinomiales inversos sobre polinomios de Ore torcidos. (Texto tomado de la fuente) | spa |
| dc.description.abstract | In this thesis we study the reflexive-nilpotents-property (RNP for short) over quantum algebras such as skew polynomial rings and skew PBW extensions. We investigate the transfer of this property between ring of coefficients and noncommutative rings of polynomial type over these rings. We consider this property for localizations by regular elements of skew PBW extensions. Related to RNP property, we study the notions of weak annihilator and nilpotent associated prime ideal, and formulate several results that extend or contribute those corresponding in the literature. Additionally, we investigate the associated prime ideals of induced modules over quantum algebras and characterize them. Our work is a contribution to an extensive research presented by different authors on ring-theoretical properties of noncommutative rings and its description of associated prime ideals. On the other hand, motivated by the research about the attached prime ideals of the inverse polynomial module over skew polynomial rings of automorphism type, and considering a very important family of quantum algebras known as skew Ore polynomials of higher order, we characterize the attached prime ideals of those modules over skew Ore polynomials. We also formulate results about the uniform dimension and the associated primes of induced modules over some families of quantum algebras. Finally, we study the couniform dimension for inverse polynomial modules over skew Ore polynomials. | eng |
| dc.description.degreelevel | Doctorado | |
| dc.description.degreename | Doctor en Ciencias - Matemáticas | |
| dc.format.extent | viii, 98 páginas | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.instname | Universidad Nacional de Colombia | spa |
| dc.identifier.reponame | Repositorio Institucional Universidad Nacional de Colombia | spa |
| dc.identifier.repourl | https://repositorio.unal.edu.co/ | spa |
| dc.identifier.uri | https://repositorio.unal.edu.co/handle/unal/88799 | |
| dc.language.iso | eng | |
| dc.publisher | Universidad Nacional de Colombia - sede Bogotá | |
| dc.publisher.branch | Universidad Nacional de Colombia - Sede Bogotá | |
| dc.publisher.faculty | Facultad de Ciencias | |
| dc.publisher.place | Bogotá, Colombia | |
| dc.publisher.program | Bogotá - Ciencias - Doctorado en Ciencias - Matemáticas | |
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| dc.rights.accessrights | info:eu-repo/semantics/openAccess | |
| dc.rights.license | Reconocimiento 4.0 Internacional | |
| dc.subject.ddc | 510 - Matemáticas | |
| dc.subject.lemb | Polinomios | spa |
| dc.subject.lemb | Polynomials | eng |
| dc.subject.lemb | Anillos (Algebra) | spa |
| dc.subject.lemb | Rings (algebra) | eng |
| dc.subject.other | Teoría de la dimensión (Álgebra) | spa |
| dc.subject.other | Dimension theory (Algebra) | eng |
| dc.subject.proposal | Skew polynomial ring | eng |
| dc.subject.proposal | skew Ore polynomials | eng |
| dc.subject.proposal | skew PBW extension | eng |
| dc.subject.proposal | semi-graded ring | eng |
| dc.subject.proposal | RNP ring | eng |
| dc.subject.proposal | associated prime | eng |
| dc.subject.proposal | weak annihilator | eng |
| dc.subject.proposal | nilpotent associated prime | eng |
| dc.subject.proposal | induced module | eng |
| dc.subject.proposal | attached prime | eng |
| dc.subject.proposal | inverse polynomial module | eng |
| dc.subject.proposal | Bass module | eng |
| dc.subject.proposal | uniform dimension | eng |
| dc.subject.proposal | couniform dimension | eng |
| dc.subject.proposal | perfect ring | eng |
| dc.title | Theory of associated and attached prime ideals over quantum algebras | eng |
| dc.title.translated | Teoría de ideales primos asociados y adjuntos sobre álgebras cuánticas | spa |
| dc.type | Trabajo de grado - Doctorado | |
| dc.type.coar | http://purl.org/coar/resource_type/c_db06 | |
| dc.type.coarversion | http://purl.org/coar/version/c_ab4af688f83e57aa | |
| dc.type.content | Text | |
| dc.type.driver | info:eu-repo/semantics/doctoralThesis | |
| dc.type.redcol | http://purl.org/redcol/resource_type/TD | |
| dc.type.version | info:eu-repo/semantics/acceptedVersion | |
| dcterms.audience.professionaldevelopment | Investigadores | |
| dcterms.audience.professionaldevelopment | Estudiantes | |
| dcterms.audience.professionaldevelopment | Maestros | |
| dcterms.audience.professionaldevelopment | Público general | |
| oaire.accessrights | http://purl.org/coar/access_right/c_abf2 |