Infinite Rings with Planar Zero-divisor Graphs
نویسنده
چکیده
For any commutative ring R that is not a domain, there is a zerodivisor graph, denoted Γ(R), in which the vertices are the nonzero zero-divisors of R and two distinct vertices x and y are joined by an edge exactly when xy = 0. In [Sm2], Smith characterized the graph structure of Γ(R) provided it is infinite and planar. In this paper, we give a ring-theoretic characterization of R such that Γ(R) is infinite and planar.
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