| dc.contributor.advisor | Trlifaj, Jan | |
| dc.creator | Pospíšil, David | |
| dc.date.accessioned | 2021-05-19T17:42:11Z | |
| dc.date.available | 2021-05-19T17:42:11Z | |
| dc.date.issued | 2009 | |
| dc.identifier.uri | http://hdl.handle.net/20.500.11956/24712 | |
| dc.description.abstract | Let R be a commutative 1-Gorenstein ring. Our main result characterizes all tilting and cotilting R-modules: up to equivalence: they are parametrized by subsets of the set of all prime ideals of height one. More precisely, every tilting (cotilting) R-module is equivalent to some Bass tilting (cotilting) module. This characterization was known in the particular case of Dedekind domains: Chapter 4 contains a new and simpler proof of this fact. Our main result is proved in Chapter 5, while Chapter 6 deals with the cotilting case. In Chapter 4, there is also a proof of the less well-known fact that all finitely generated tilting modules over commutative rings are projective. | en_US |
| dc.language | Čeština | cs_CZ |
| dc.language.iso | cs_CZ | |
| dc.publisher | Univerzita Karlova, Matematicko-fyzikální fakulta | cs_CZ |
| dc.title | Vychylující moduly nad Gorensteinovými okruhy | cs_CZ |
| dc.type | rigorózní práce | cs_CZ |
| dcterms.created | 2009 | |
| dcterms.dateAccepted | 2009-11-19 | |
| dc.description.department | Department of Algebra | en_US |
| dc.description.department | Katedra algebry | cs_CZ |
| dc.description.faculty | Faculty of Mathematics and Physics | en_US |
| dc.description.faculty | Matematicko-fyzikální fakulta | cs_CZ |
| dc.identifier.repId | 79715 | |
| dc.title.translated | Tilting Modules over Gorenstein Rings | en_US |
| dc.identifier.aleph | 000864473 | |
| thesis.degree.name | RNDr. | |
| thesis.degree.level | rigorózní řízení | cs_CZ |
| thesis.degree.discipline | Mathematical structures | en_US |
| thesis.degree.discipline | Matematické struktury | cs_CZ |
| thesis.degree.program | Mathematics | en_US |
| thesis.degree.program | Matematika | cs_CZ |
| uk.thesis.type | rigorózní 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 | Matematické struktury | cs_CZ |
| uk.degree-discipline.en | Mathematical structures | en_US |
| uk.degree-program.cs | Matematika | cs_CZ |
| uk.degree-program.en | Mathematics | en_US |
| thesis.grade.cs | Uznáno | cs_CZ |
| thesis.grade.en | Recognized | en_US |
| uk.abstract.en | Let R be a commutative 1-Gorenstein ring. Our main result characterizes all tilting and cotilting R-modules: up to equivalence: they are parametrized by subsets of the set of all prime ideals of height one. More precisely, every tilting (cotilting) R-module is equivalent to some Bass tilting (cotilting) module. This characterization was known in the particular case of Dedekind domains: Chapter 4 contains a new and simpler proof of this fact. Our main result is proved in Chapter 5, while Chapter 6 deals with the cotilting case. In Chapter 4, there is also a proof of the less well-known fact that all finitely generated tilting modules over commutative rings are projective. | en_US |
| uk.file-availability | V | |
| uk.grantor | Univerzita Karlova, Matematicko-fyzikální fakulta, Katedra algebry | cs_CZ |
| thesis.grade.code | U | |
| uk.publication-place | Praha | cs_CZ |
| uk.thesis.defenceStatus | U | |
| dc.identifier.lisID | 990008644730106986 | |
