夏良忠Hsia, Liang-Chung林詠翔Lin, Yong-Siang2025-12-092025-06-092025https://etds.lib.ntnu.edu.tw/thesis/detail/016a7919f3c7956ae289b19e2ccb1a79/http://rportal.lib.ntnu.edu.tw/handle/20.500.12235/125502noneIn 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.noneidempotentmatrix ringorthomodular posetHamiltonian cycleSperner property學術論文