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| Paper IPM / M / 14180 |
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| Abstract: | |||||
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Let R be a finite commutative ring with nonzero identity and denote its
Jacobson radical by J(R). The Jacobson graph of R is the graph in which
the vertex set is R\J(R), and two distinct vertices x and y
are adjacent if and only if 1−xy is not a unit in R. In this paper, up
to isomorphism, we classify the rings R whose Jacobson graphs are
toroidal.
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