Homological dimensions and special classes of rings
| Thesis title in Czech: | Homologické dimenze a speciální třídy okruhů |
|---|---|
| Thesis title in English: | Homological dimensions and special classes of rings |
| English key words: | Regular ring|Gorenstein ring|Global dimension|Gorenstein homological algebra |
| Academic year of topic announcement: | 2023/2024 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | angličtina |
| Department: | Department of Algebra (32-KA) |
| Supervisor: | Liran Shaul, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 02.03.2024 |
| Date of assignment: | 04.03.2024 |
| Confirmed by Study dept. on: | 04.03.2024 |
| Opponents: | Souvik Dey, Ph.D. |
| Guidelines |
| The student will investigate different dimension of modules and use them to characterize special homological classes of commutative rings.
The student will characterize regular local rings as those with finite global dimension and Gorenstein rings as those with finite Gorenstein global dimension. |
| References |
| * Matsumura, H. (1989). Commutative ring theory (No. 8). Cambridge university press.
* Eisenbud, D. (2013). Commutative algebra: with a view toward algebraic geometry (Vol. 150). Springer Science & Business Media. * Christensen, L. W. (2000). Gorenstein dimensions (No. 1747). Springer Science & Business Media. |