Hofman, Merel (2025) Linear algebraic crowds. Bachelor's Thesis, Mathematics.
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Abstract
Crowds are generalizations of groups, and bands are generalizations of commutative rings. In this thesis, we continue the study of these crowds, with a focus on some linear algebraic crowds, namely the special linear group and general linear group over bands. We start the thesis by introducing bands and crowds and giving some general results. We then study the special and general linear groups over a band B, SLn(B) and GLn(B), and their comparison, with case studies for the Krasner hyperfield and the sign hyperfield. We follow this by defining the semidirect product of crowds, and the crowd version of the short exact sequence, which we use to learn more about SLn(B) and GLn(B).
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Lorscheid, O. and Salgado Guimaraes da Silva, C. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 24 Jul 2025 10:46 |
| Last Modified: | 25 Jul 2025 13:13 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/36359 |
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