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Paper IPM / M / 14163  


Abstract:  
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, the
nonorientable genus of some Jacobson graphs is either computed or estimated
by a lower bound. As an application, the rings R with projective Jacobson
graphs are classified.
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