Realization of refinement monoids
| Thesis title in Czech: | Realizace zjemňujících monoidů |
|---|---|
| Thesis title in English: | Realization of refinement monoids |
| Key words: | von Neumnnovsky regulární okruh|zjemňující monoid|problém realizace |
| English key words: | von Neumann regular ring|refinement monoid|realization problem |
| Academic year of topic announcement: | 2020/2021 |
| Thesis type: | diploma thesis |
| Thesis language: | angličtina |
| Department: | Department of Algebra (32-KA) |
| Supervisor: | doc. Mgr. Pavel Růžička, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 30.09.2020 |
| Date of assignment: | 30.09.2020 |
| Confirmed by Study dept. on: | 23.11.2020 |
| Date and time of defence: | 15.09.2021 09:00 |
| Date of electronic submission: | 22.07.2021 |
| Date of submission of printed version: | 22.07.2021 |
| Date of proceeded defence: | 15.09.2021 |
| Opponents: | prof. RNDr. Jan Trlifaj, CSc., DSc. |
| Guidelines |
| Cílem práce bude zpracovat některé z dosavadních výsledků týkajících se realizace zjemňujících monoidů Grothendieckovými monoidy von Neumannovsky regulárních okruhů. Student by se měl zaměřit především na nedávný výsledek Ary, Bosy a Parda, že každý konečně generovaný kónický zjemňující monoid je realizovatelný. |
| References |
| 1. Ara P.: The regular algebra of a poset. Trans. Am. Math. Soc. 362(3), 1505–1546 (2010)
3. Ara P., Bosa J., Pardo E.: Refinement monoids and adaptable separated graphs. Semigroup Forum (2019). 4. Ara P., Bosa J., Pardo E., Sims A.: The groupoids of adaptable separated graphs and their type semigroups. Int. Math. Res. Not. IMRN (2020). 1. Ara P., Bosa J., Pardo E.: The realization problem for finitely generated refinement monoids, Selecta Mathematica vol. 26, (2020) 5. Ara P., Brustenga M.: The regular algebra of a quiver. J. Algebra 309, 207–235 (2007) 6. Ara P., Exel R.: Dynamical systems associated to separated graphs, graph algebras, and paradoxical decompositions. Adv. Math. 252, 748–804 (2014) 7. Ara P., Goodearl K.R.: Leavitt path algebras of separated graphs. J. Reine Angew. Math. 669, 165–224 (2012) 8. Ara P., Goodearl K.R.: Tame and wild refinement monoids. Semigroup Forum 91, 1–27 (2015) 9. Ara P., Goodearl K.R.: The realization problem for some wild monoids and the Atiyah problem. Trans. Am. Math. Soc. 369, 5665–5710 (2017) |
| Preliminary scope of work in English |
| The thesis should survey the realization problem for refinement monoids in Grothendieck monoids of von Neumann regular rings. The student should focus on the recent result of Ara, Bosa, and Pardo that every finitely generated conical refinement monoid has a realization. |