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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Matraś, A., Siemaszko, A. The Cayley Property of Some Distant Graphs and Relationship with the Stern–Brocot Tree. Results Math 73, 141 (2018). https://doi.org/10.1007/s00025-018-0904-8
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DOI: https://doi.org/10.1007/s00025-018-0904-8