Abstract
One of the graphs associated with any ring R is its distant graph G(R,Delta ) with points of the projective line mathbb {P}(R) over R as vertices. We prove that the distant graph of any commutative, Artinian ring is a Cayley graph. The main result is the fact that G(mathbb Z,Delta ) is a Cayley graph of a non-artinian commutative ring. We indicate two non-isomorphic subgroups of PSL_2(mathbb Z) corresponding to this graph.
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