矩陣環上的等冪元所形成的偏序集
| dc.contributor | 夏良忠 | zh_TW |
| dc.contributor | Hsia, Liang-Chung | en_US |
| dc.contributor.author | 林詠翔 | zh_TW |
| dc.contributor.author | Lin, Yong-Siang | en_US |
| dc.date.accessioned | 2025-12-09T08:11:41Z | |
| dc.date.available | 2025-06-09 | |
| dc.date.issued | 2025 | |
| dc.description.abstract | none | zh_TW |
| dc.description.abstract | In this thesis, we introduce a partial order relation on the set of idempotents in a ring. Especially, we characterize this poset structure and some algebraic properties on the matrix ring over a division ring. Also, we give a concrete example of this poset on the ring of $3\\times 3$ matrices over $\\mathbb{F}_2$ and make a combinatorial conjecture. In addition, we give some methods to construct idempotent matrices. | en_US |
| dc.description.sponsorship | 數學系 | zh_TW |
| dc.identifier | 61040008S-46975 | |
| dc.identifier.uri | https://etds.lib.ntnu.edu.tw/thesis/detail/016a7919f3c7956ae289b19e2ccb1a79/ | |
| dc.identifier.uri | http://rportal.lib.ntnu.edu.tw/handle/20.500.12235/125502 | |
| dc.language | 英文 | |
| dc.subject | none | zh_TW |
| dc.subject | idempotent | en_US |
| dc.subject | matrix ring | en_US |
| dc.subject | orthomodular poset | en_US |
| dc.subject | Hamiltonian cycle | en_US |
| dc.subject | Sperner property | en_US |
| dc.title | 矩陣環上的等冪元所形成的偏序集 | zh_TW |
| dc.title | Partial Order on Idempotents in Matrix Ring | en_US |
| dc.type | 學術論文 |
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