Konečně generované polookruhy a polotělesa
| Thesis title in Czech: | Konečně generované polookruhy a polotělesa |
|---|---|
| Thesis title in English: | Finitely generated semirings and semifields |
| Key words: | ideal-simple semirings|finitely generated semirings|parasemifields|semifields |
| English key words: | ideálově-jednoduché polookruhy|konečně generované polookruhy|parapolotělesa|polotělesa |
| Academic year of topic announcement: | 2020/2021 |
| Thesis type: | diploma thesis |
| Thesis language: | čeština |
| Department: | Department of Algebra (32-KA) |
| Supervisor: | doc. Mgr. Vítězslav Kala, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 29.10.2020 |
| Date of assignment: | 29.10.2020 |
| Confirmed by Study dept. on: | 23.11.2020 |
| Date and time of defence: | 23.06.2021 09:00 |
| Date of electronic submission: | 21.05.2021 |
| Date of submission of printed version: | 21.05.2021 |
| Date of proceeded defence: | 23.06.2021 |
| Opponents: | RNDr. Miroslav Korbelář, Ph.D. |
| Guidelines |
| The main goal of the thesis is to write down the proof of the classification of finitely generated ideal-simple semirings (with full details), based on the articles [1] - [4]. The student may then possibly further study related questions, e.g., in the situation of Banach semifields [5]. |
| References |
| [1] R. El Bashir, J. Hurt, A.Jančařík, T. Kepka, Simple commutative semirings, Journal of Algebra 236 (2001), 277 - 306.
[2] J. Ježek, V. Kala, T. Kepka, Finitely generated algebraic structures with various divisibility conditions, Forum Math. 24 (2012), 379 - 397. [3] V. Kala, Lattice-ordered abelian groups finitely generated as semirings, J. Commut. Algebra 9 (2017), 387 - 412. [4] V. Kala, M. Korbelář, Idempotence of finitely generated commutative semifields, Forum Math. 30 (2018), 1461 - 1474. [5] E. Leichtnam, A classification of the commutative Banach perfect semi-fields of characteristic 1: applications, Math. Ann. 369 (2017), 653 - 703. |