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A Note on Idempotent Matrices: The Poset Structure and The Construction
Sen-Peng Eu, Yong-Siang Lin, Wei-Liang Sun
https://arxiv.org/abs/2510.09501 https://

A Note on Idempotent Matrices: The Poset Structure and The Construction
Idempotent elements play a fundamental role in ring theory, as they encode significant information about the underlying algebraic structure. In this paper, we study idempotent matrices from two perspectives. First, we analyze the partially ordered set of idempotents in matrix rings over a division ring. We characterize the partial order relation explicitly in terms of block decompositions of idempotent matrices. Second, over principal ideal domains, we establish an equivalent condition for a ma…

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