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Serreho hypotéza o projektivních modulech nad okruhy polynomů
dc.contributor.advisorShaul, Liran
dc.creatorYoung, Edward
dc.date.accessioned2023-07-24T12:19:26Z
dc.date.available2023-07-24T12:19:26Z
dc.date.issued2023
dc.identifier.urihttp://hdl.handle.net/20.500.11956/182987
dc.description.abstractThis is an expository paper on the Quillen-Suslin Theorem, formerly known as Serre's Conjecture. A self-contained proof of this theorem is presented, followed by a discussion of the related Bass-Quillen Conjecture. The first chapter establishes the necessary theory, building on undergraduate algebra with the essentials of free, projective, and flat modules. The second chapter presents a complete proof of the theorem, dealing with regular rings, stably-free modules, and the related calculus of unimodular rows. The third and final chapter lists partial results surrounding the as yet unresolved Bass-Quillen Conjecture, offering brief explanations and suggestions for further reading. 1en_US
dc.languageEnglishcs_CZ
dc.language.isoen_US
dc.publisherUniverzita Karlova, Matematicko-fyzikální fakultacs_CZ
dc.subjectprojective|module|commutative algebra|tensor product|polynomial ringen_US
dc.subjectprojektivní|modul|komutativní algebra|tenzor|okruhy polynomůcs_CZ
dc.titleSerre's conjecture on projective modules over polynomial ringsen_US
dc.typebakalářská prácecs_CZ
dcterms.created2023
dcterms.dateAccepted2023-06-28
dc.description.departmentKatedra algebrycs_CZ
dc.description.departmentDepartment of Algebraen_US
dc.description.facultyFaculty of Mathematics and Physicsen_US
dc.description.facultyMatematicko-fyzikální fakultacs_CZ
dc.identifier.repId207923
dc.title.translatedSerreho hypotéza o projektivních modulech nad okruhy polynomůcs_CZ
dc.contributor.refereeBird, Isaac
thesis.degree.nameBc.
thesis.degree.levelbakalářskécs_CZ
thesis.degree.disciplineObecná matematikacs_CZ
thesis.degree.disciplineGeneral Mathematicsen_US
thesis.degree.programObecná matematikacs_CZ
thesis.degree.programGeneral Mathematicsen_US
uk.thesis.typebakalářská prácecs_CZ
uk.taxonomy.organization-csMatematicko-fyzikální fakulta::Katedra algebrycs_CZ
uk.taxonomy.organization-enFaculty of Mathematics and Physics::Department of Algebraen_US
uk.faculty-name.csMatematicko-fyzikální fakultacs_CZ
uk.faculty-name.enFaculty of Mathematics and Physicsen_US
uk.faculty-abbr.csMFFcs_CZ
uk.degree-discipline.csObecná matematikacs_CZ
uk.degree-discipline.enGeneral Mathematicsen_US
uk.degree-program.csObecná matematikacs_CZ
uk.degree-program.enGeneral Mathematicsen_US
thesis.grade.csVýborněcs_CZ
thesis.grade.enExcellenten_US
uk.abstract.enThis is an expository paper on the Quillen-Suslin Theorem, formerly known as Serre's Conjecture. A self-contained proof of this theorem is presented, followed by a discussion of the related Bass-Quillen Conjecture. The first chapter establishes the necessary theory, building on undergraduate algebra with the essentials of free, projective, and flat modules. The second chapter presents a complete proof of the theorem, dealing with regular rings, stably-free modules, and the related calculus of unimodular rows. The third and final chapter lists partial results surrounding the as yet unresolved Bass-Quillen Conjecture, offering brief explanations and suggestions for further reading. 1en_US
uk.file-availabilityV
uk.grantorUniverzita Karlova, Matematicko-fyzikální fakulta, Katedra algebrycs_CZ
thesis.grade.code1
uk.publication-placePrahacs_CZ
uk.thesis.defenceStatusO


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