Rank Two Commutative Semifields
| Thesis title in Czech: | Komutativní polotělesa hodnosti dva |
|---|---|
| Thesis title in English: | Rank Two Commutative Semifields |
| Key words: | konečná|komutativní|polotělesa|vektorový|prostor |
| English key words: | finite|commutative|semifields|vector|space |
| Academic year of topic announcement: | 2021/2022 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | angličtina |
| Department: | Department of Algebra (32-KA) |
| Supervisor: | doc. Faruk Göloglu, Dr. rer. nat. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 18.04.2022 |
| Date of assignment: | 20.04.2022 |
| Confirmed by Study dept. on: | 18.07.2022 |
| Date and time of defence: | 06.09.2022 10:00 |
| Date of electronic submission: | 21.07.2022 |
| Date of submission of printed version: | 25.07.2022 |
| Date of proceeded defence: | 06.09.2022 |
| Opponents: | doc. Mgr. Pavel Růžička, Ph.D. |
| Guidelines |
| An important problem in the theory of finite semifields is the classification of
"rank two commutative semifields," i.e., semifields that are (at most) two dimensional over their middle nuclei. Cohen and Ganley [1] showed that existence of such semifields can be explained via a specific type of representation, gave an infinite family when the characteristic is 3, showed in characteristic 2 there are no examples other than finite fields. The student should explain this important paper concentrating on the odd characteristic case. The thesis should also contain newer results that show nonexistence in certain cases [2]. |
| References |
| [1] S. D. COHEN AND M. J. GANLEY, Commutative semifields, two-dimensional over their
middle nuclei, J. Algebra, 75 (1982), pp. 373–385. [2] A. BLOKHUIS , M. LAVRAUW, AND S. BALL, On the classification of semifield flocks, Adv. Math., 180 (2003), pp. 104–111. |