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dc.rights.licenseAtribución-NoComercial-SinDerivadas 4.0 Internacional
dc.contributor.advisorReyes, Armando
dc.contributor.authorRamírez Cubillos, María Camila
dc.date.accessioned2020-03-06T20:09:41Z
dc.date.available2020-03-06T20:09:41Z
dc.date.issued2019-10
dc.identifier.urihttps://repositorio.unal.edu.co/handle/unal/75953
dc.description.abstractEn el presente trabajo estudiamos los ideales primos asociados de algunos anillos no conmutativos de tipo polinomial. En la literatura encontramos que estos ideales fueron caracterizados en un primer trabajo por Brewer y Heinzer (1974), donde ellos muestran que los ideales primos asociados de un anillo de polinomios sobre un anillo R pueden ser extendidos a partir de los ideales primos asociados de R. A partir de esto, diferentes autores han extendido este resultado para otras estructuras como lo hizo Annin (2004) desarrollando su trabajo sobre las extensiones de Ore. Otro trabajo que resaltamos es el realizado por Bhat (2010) en donde él caracterizó los ideales primos asociados sobre anillos $\sigma$-rígidos débiles. A partir de los resultados encontrados en la literatura, en este trabajo extendemos estos trabajos para las extensiones PBW torcidas introducidas por Gallego y Lezama (2011). Nosotros desarrollamos nuestro trabajo en dos partes: primero, extendemos los resultados de (2004) para las extensiones PBW torcidas. Con este objetivo en mente, presentamos algunas propiedades de esta estructura bajo la condición de $(\Sigma, \Delta)$-compatibilidad (definida en Hashemi, Khalil and Alhevaz (2017) y Reyes and Suarez (2018)) y definimos la noción de anulador complaciente (noción definida por Annin (2004) para extensiones de Ore) sobre las extensiones PBW torcidas. Como una segunda parte, extendemos los resultados de Bhat (2010), para las extensiones PBW torcidas sobre anillos $\Sigma$-rígidos débiles introducidos en Reyes and Suarez (2018).
dc.description.abstractIn this work we study the associated prime ideals of some noncommutative rings of polynomial type. In the literature we find that these ideals were characterized in a first work by Brewer and Heinzer (1974), where they shown that the associated prime ideals of a polynomial ring over a ring R can be extended from the associated prime ideals of R. From that, different authors have extended this result to other structures as Annin did in (2004) developing his work over Ore extensions. Another work that we highlight be the one carried out by Bhat (2010) where he characterized the associated prime ideals over weak $\sigma$-rigid rings. From the results found in the literature, in this work we extend these works for the skew PBW extensions introduced by Gallego and Lezama (2011). We develop our work in two parts: first, we extend the results of Annin (2004) for skew PBW extensions. With this objective in mind, we present some properties of this structure under the condition of $(\Sigma, \Delta)$-compatibility (defined in Hashemi, Khalil and Alhevaz (2017) and Reyes and Suarez (2018)), and we define the notion of annihilator-compliant (notion defined by Annin in (2004) for Ore extensions) for the context of skew PBW extensions. As a second part, we extend the results of Bhat (2010) for the skew PBW extensions over weak $\Sigma$-rigid rings introduced in Reyes and Suarez (2018).
dc.format.extent55
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.rightsDerechos reservados - Universidad Nacional de Colombia
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject.ddcMatemáticas::Álgebra
dc.titleAssociated prime ideals of noncommutative rings of polynomials type
dc.title.alternativeIdeales primos asociados de anillos noconmutativos de tipo polinomial
dc.typeOtro
dc.rights.spaAcceso abierto
dc.description.additionalMagíster en Ciencias en Matemáticas
dc.type.driverinfo:eu-repo/semantics/other
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
dc.description.degreelevelMaestría
dc.publisher.departmentDepartamento de Matemáticas
dc.publisher.branchUniversidad Nacional de Colombia - Sede Bogotá
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dc.rights.accessrightsinfo:eu-repo/semantics/openAccess
dc.subject.proposalIdeal primo asociado
dc.subject.proposalAssociated prime ideal
dc.subject.proposalAnillo no conmutativo
dc.subject.proposalNoncommutative ring
dc.subject.proposalSkew PBW extension
dc.subject.proposalExtensión PBW torcida
dc.subject.proposalAnillo compatible
dc.subject.proposalCompatible ring
dc.subject.proposalAnillo $\Sigma$-rígido débil
dc.subject.proposalWeak $\Sigma$-rigid ring
dc.type.coarhttp://purl.org/coar/resource_type/c_1843
dc.type.coarversionhttp://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.contentText
oaire.accessrightshttp://purl.org/coar/access_right/c_abf2


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Atribución-NoComercial-SinDerivadas 4.0 InternacionalThis work is licensed under a Creative Commons Reconocimiento-NoComercial 4.0.This document has been deposited by the author (s) under the following certificate of deposit