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| Paper IPM / M / 7380 |
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| Abstract: | |||||
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Let R be a non-commutative ring. The commuting graph of R
denoted by Γ(R), is a graph with vertex set R\Z(R), and two distinct vertices a and b are adjacent if
ab=ba. In this paper we investigate some properties of
Γ(R), whenever R is a finite semisimple ring. For any
finite field F, we obtain a minimum degree, maximum degree and
clique number of Γ(Mn(F)). Also it is shown that for any
two finite semisimple rings R and S, if
Γ(R) ≅ Γ(S),then there are commutative semisimple
ring R1 and S1 and semisimple ring T such that R ≅ T×R1, S ≅ T×S1 and |R1|=|S1|.
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