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|Paper IPM / M / 11317||
The commuting graph of a ring R, denoted by
\mathnormalΓ(R), is a graph whose vertices are all
noncentral elements of R and two distinct vertices are joint by an edge whenever
they commute. It is conjectured that
if R is a ring with identity such that \mathnormalΓ(R) ≅ \mathnormalΓ(Mn(F)),
for a finite field F and n ≥ 2, then R ≅ Mn(F).
Here we prove this conjecture when n=2.
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