A note on commuting graphs of matrix rings over fields

2015/01/05 by C. Miguel, Miguel, C.
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA

paper · pdf · doi:10.48550/arxiv.1501.01030

openalex publication_date 2015/01/05 · arxiv created 2015/03/01 · arxiv updated 2015/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We will give a short proof of the fact that if the algebraic closure of a field \mathbb F is a finite extension, then for n≥ 3 the commuting graph Γ(M_n(\mathbb F)) is connected and its diameter is four.

Citations

• On the diameter of the commuting graph of the full matrix ring over the real numbers

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