| dc.contributor.advisor | Shaul, Liran | |
| dc.creator | Young, Edward | |
| dc.date.accessioned | 2023-07-24T12:19:26Z | |
| dc.date.available | 2023-07-24T12:19:26Z | |
| dc.date.issued | 2023 | |
| dc.identifier.uri | http://hdl.handle.net/20.500.11956/182987 | |
| dc.description.abstract | This 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. 1 | en_US |
| dc.language | English | cs_CZ |
| dc.language.iso | en_US | |
| dc.publisher | Univerzita Karlova, Matematicko-fyzikální fakulta | cs_CZ |
| dc.subject | projective|module|commutative algebra|tensor product|polynomial ring | en_US |
| dc.subject | projektivní|modul|komutativní algebra|tenzor|okruhy polynomů | cs_CZ |
| dc.title | Serre's conjecture on projective modules over polynomial rings | en_US |
| dc.type | bakalářská práce | cs_CZ |
| dcterms.created | 2023 | |
| dcterms.dateAccepted | 2023-06-28 | |
| dc.description.department | Katedra algebry | cs_CZ |
| dc.description.department | Department of Algebra | en_US |
| dc.description.faculty | Faculty of Mathematics and Physics | en_US |
| dc.description.faculty | Matematicko-fyzikální fakulta | cs_CZ |
| dc.identifier.repId | 207923 | |
| dc.title.translated | Serreho hypotéza o projektivních modulech nad okruhy polynomů | cs_CZ |
| dc.contributor.referee | Bird, Isaac | |
| thesis.degree.name | Bc. | |
| thesis.degree.level | bakalářské | cs_CZ |
| thesis.degree.discipline | Obecná matematika | cs_CZ |
| thesis.degree.discipline | General Mathematics | en_US |
| thesis.degree.program | Obecná matematika | cs_CZ |
| thesis.degree.program | General Mathematics | en_US |
| uk.thesis.type | bakalářská práce | cs_CZ |
| uk.taxonomy.organization-cs | Matematicko-fyzikální fakulta::Katedra algebry | cs_CZ |
| uk.taxonomy.organization-en | Faculty of Mathematics and Physics::Department of Algebra | en_US |
| uk.faculty-name.cs | Matematicko-fyzikální fakulta | cs_CZ |
| uk.faculty-name.en | Faculty of Mathematics and Physics | en_US |
| uk.faculty-abbr.cs | MFF | cs_CZ |
| uk.degree-discipline.cs | Obecná matematika | cs_CZ |
| uk.degree-discipline.en | General Mathematics | en_US |
| uk.degree-program.cs | Obecná matematika | cs_CZ |
| uk.degree-program.en | General Mathematics | en_US |
| thesis.grade.cs | Výborně | cs_CZ |
| thesis.grade.en | Excellent | en_US |
| uk.abstract.en | This 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. 1 | en_US |
| uk.file-availability | V | |
| uk.grantor | Univerzita Karlova, Matematicko-fyzikální fakulta, Katedra algebry | cs_CZ |
| thesis.grade.code | 1 | |
| uk.publication-place | Praha | cs_CZ |
| uk.thesis.defenceStatus | O | |
