矩陣環上的等冪元所形成的偏序集
No Thumbnail Available
Date
2025
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
none
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.
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.
Description
Keywords
none, idempotent, matrix ring, orthomodular poset, Hamiltonian cycle, Sperner property