In this paper we consider, for a finite commutative ring R, the well-studied zero-divisor graph Γ(R) and the compressed zero-divisor graph Γc(R) of R and a newly-defined graphical structure --- the zero-divisor lattice Λ(R) of R. We give results which provide information when Γ(R) ≅ Γ(S), Γc(R) ≅ Γc(S), and Λ(R) ≅ Λ(S) for two finite commutative rings R and S. We also provide a theorem which says that Λ(R) is almost always connected.

Author Bio

Darrin Weber is a senior mathematics major at Millikin University and will be graduating in May of 2011. After graduation, he plans on attending graduate school to pursue a Ph.D. in theoretical mathematics.