Ela on C−commuting Graph of Matrix Algebra∗
نویسنده
چکیده
Let D be a division ring, n 2 a natural number, and C ⊆ Mn(D). Two matrices A and B are called C−commuting if there is C ∈ C that AB−BA = C. In this paper the C−commuting graph of Mn(D) is defined and denoted by ΓC(Mn(D)). Conditions are given that guarantee that the C−commuting graph is connected.
منابع مشابه
On the diameter of the commuting graph of the full matrix ring over the real numbers
In a recent paper C. Miguel proved that the diameter of the commuting graph of the matrix ring $mathrm{M}_n(mathbb{R})$ is equal to $4$ if either $n=3$ or $ngeq5$. But the case $n=4$ remained open, since the diameter could be $4$ or $5$. In this work we close the problem showing that also in this case the diameter is $4$.
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