On the Galois theories and categorical aspects of strongly normal extensions

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dc.contributor.advisorBlázquez Sanz, David
dc.contributor.authorRuiz Castrillon, Juan Felipe
dc.date.accessioned2024-10-24T19:01:06Z
dc.date.available2024-10-24T19:01:06Z
dc.date.issued2023
dc.description.abstractDifferential algebra study differential equations from an algebraic point of view, it was introduced by Joseph Ritt saying that a differential algebraic structure(ring, field, algebra) is the structure joint of a finitely set of derivations. Later the notion of Strongly Normal Extension was introduced by Kolchin [11] and more recently by Jerald Kovacic [4, 5]. (Tomado de la fuente)eng
dc.description.abstractEl álgebra diferencial estudia las ecuaciones diferenciales desde un punto de vista algebraico. Fue introducida por Joseph Ritt, quien afirmó que una estructura algebraico-diferencial (anillo, campo, álgebra) es una estructura algebraico junto a un conjunto finito de derivaciones. Posteriormente, la noción de Extensión Fuertemente Normal fue introducida por Kolchin [11] y más recientemente por Jerald Kovacic [4, 5].spa
dc.description.curricularareaMatemáticas.Sede Medellínspa
dc.description.degreelevelMaestríaspa
dc.description.degreenameMagíster en Ciencias - Matemáticasspa
dc.description.notesÁlgebra, algebra
dc.description.technicalinfoÁlgebra Diferencial, Differential algebra
dc.format.extent48 páginasspa
dc.format.mimetypeapplication/pdfspa
dc.identifier.instnameUniversidad Nacional de Colombiaspa
dc.identifier.reponameRepositorio Institucional Universidad Nacional de Colombiaspa
dc.identifier.repourlhttps://repositorio.unal.edu.co/spa
dc.identifier.urihttps://repositorio.unal.edu.co/handle/unal/87042
dc.language.isoengspa
dc.publisherUniversidad Nacional de Colombiaspa
dc.publisher.branchUniversidad Nacional de Colombia - Sede Medellínspa
dc.publisher.facultyFacultad de Cienciasspa
dc.publisher.placeMedellín, Colombiaspa
dc.publisher.programMedellín - Ciencias - Maestría en Ciencias - Matemáticasspa
dc.relation.indexedLaReferenciaspa
dc.relation.referencesA. Ovchinnikov. Differential Algebra, Notes. 2015.spa
dc.relation.referencesJ. M. Liou. Differential Rings, Notes. 2015.spa
dc.relation.referencesP. Morandi. Field and Galois Theory, Springer-Verlag New York. 1996.spa
dc.relation.referencesJ. Kovacic. The Differential Galois Theory of Strongly Normal Extensions, Transactions of the American Mathematical Society. 2003.spa
dc.relation.referencesJ. Kovacic. Geometric Characterization of Strongly Normal Extensions, Transactions of the American Mathematical Society. 2005.spa
dc.relation.referencesB. Poizat. A course in Model Theory, Springer New York. 2000.spa
dc.relation.referencesP. Landesman. Generalized Differential Galois Theory , Transactions of the American Mathematical Society. 2008.spa
dc.relation.referencesO. Sánchez. Relative D-Groups and Differential Galois Theory in Several Derivations, Transactions of the American Mathematical Society. 2015.spa
dc.relation.referencesM. Sweedler. The predual theorem to the Jacobson-Bourbaki theorem, Transactions of the American Mathematical Society. 1975.spa
dc.relation.referencesD. Marker. Introduction to Model Theory, Model Theory, Algebra and Geometry MSRI Publications. 2000.spa
dc.relation.referencesKolchin. Differential algebra and algebraic groups, Pure and Applied Mathematics, Academic Press, New York-London. 1973.spa
dc.relation.referencesKolchin. Galois Theory of Differential Fields, American Journal of Mathematics. 1953.spa
dc.relation.referencesI. Kaplansky. An Introduction to Differential Algebra, Hermann. 1976.spa
dc.relation.referencesJ. Nagloo, D. Penazzi. A Note on Integrability and Internality in DCF0, arXiv:1212.4753. 2012.spa
dc.relation.referencesD. Marker. Model Theory: an Introduction, Springer New York, New York. 2002.spa
dc.relation.referencesM. Rosenlicht. Some Basic Theorems on Algebraic Groups, American Journal of Mathematics. 1956.spa
dc.relation.referencesM. Nagata. Field theory, Marcel Dekker. 1977.spa
dc.relation.referencesA. Pillay. Differential Galois Theory, Illinois Journal of Mathematics. 1998.spa
dc.rights.accessrightsinfo:eu-repo/semantics/openAccessspa
dc.rights.licenseAtribución-NoComercial 4.0 Internacionalspa
dc.rights.urihttp://creativecommons.org/licenses/by-nc/4.0/spa
dc.subject.ddc510 - Matemáticasspa
dc.subject.ddc510 - Matemáticas::512 - Álgebraspa
dc.subject.lembTeoría de Galois
dc.subject.lembTeoría de ecuaciones
dc.subject.lembAlgebra diferencial
dc.subject.lembEcuaciones diferenciales
dc.subject.proposalálgebraeng
dc.subject.proposalDerivationeng
dc.subject.proposalExtensioneng
dc.subject.proposalDerivaciónspa
dc.subject.proposalExtensiónspa
dc.titleOn the Galois theories and categorical aspects of strongly normal extensionseng
dc.title.translatedSobre las teorías de Galois y los aspectos categóricos de las extensiones fuertemente normalesspa
dc.typeTrabajo de grado - Maestríaspa
dc.type.coarhttp://purl.org/coar/resource_type/c_bdccspa
dc.type.coarversionhttp://purl.org/coar/version/c_ab4af688f83e57aaspa
dc.type.contentTextspa
dc.type.driverinfo:eu-repo/semantics/masterThesisspa
dc.type.redcolhttp://purl.org/redcol/resource_type/TMspa
dc.type.versioninfo:eu-repo/semantics/acceptedVersionspa
dcterms.audience.professionaldevelopmentEstudiantesspa
dcterms.audience.professionaldevelopmentInvestigadoresspa
dcterms.audience.professionaldevelopmentMaestrosspa
oaire.accessrightshttp://purl.org/coar/access_right/c_abf2spa

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