Article ID Journal Published Year Pages File Type
4598365 Journal of Pure and Applied Algebra 2007 8 Pages PDF
Abstract

For a commutative ring RR with zero-divisors Z(R)Z(R), the zero-divisor graph of RR is Γ(R)=Z(R)−{0}Γ(R)=Z(R)−{0}, with distinct vertices xx and yy adjacent if and only if xy=0xy=0. In this paper, we characterize when either diam(Γ(R))≤2 or gr(Γ(R))≥4. We then use these results to investigate the diameter and girth for the zero-divisor graphs of polynomial rings, power series rings, and idealizations.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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