Symmetric terms
| Thesis title in Czech: | Symetrické termy |
|---|---|
| Thesis title in English: | Symmetric terms |
| Key words: | universální algebra|symetrické termy|symetrické relace|symetrické podprostory |
| English key words: | universal algebra|symmetric terms|symmetric relations|symmetric subspaces |
| Academic year of topic announcement: | 2022/2023 |
| Thesis type: | diploma thesis |
| Thesis language: | angličtina |
| Department: | Department of Algebra (32-KA) |
| Supervisor: | doc. Mgr. Libor Barto, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 04.11.2022 |
| Date of assignment: | 04.11.2022 |
| Confirmed by Study dept. on: | 15.12.2022 |
| Date and time of defence: | 06.09.2023 09:00 |
| Date of electronic submission: | 20.07.2023 |
| Date of submission of printed version: | 24.07.2023 |
| Date of proceeded defence: | 06.09.2023 |
| Opponents: | Michael Kompatscher, Ph.D. |
| Guidelines |
| The existence of a non-trivial system of height one identities is, for finite algebras, known to be equivalent to numerous concrete height one conditions, including the existence of a cyclic term or the existence of a weak near unanimity term. It is known that the existence of a fully symmetric term is too strong, but it is consistent with the current knowledge that the existence of a term, which is fully symmetric with respect to two-variable evaluations, works. The thesis will explore this possibility. |
| References |
| C. Bergman: Universal Algebra: Fundamentals and Selected Topics, Chapman & Hall Pure and Applied Mathematics, 2011
L. Barto, Z. Brady, A. Bulatov, M. Kozik, D. Zhuk, Minimal Taylor Algebras as a Common Framework for the Three Algebraic Approaches to the CSP, 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 2021 Z. Brady: Notes on CSPs and Polymorphisms, arXiv 2210.07383, 2022 |