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.
Joe Stickles, Department of Mathematics, Millikin University JStickles@mail.millikin.edu
"Zero-Divisor Graphs and Lattices of Finite Commutative Rings,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 12
, Article 4.
Available at: http://scholar.rose-hulman.edu/rhumj/vol12/iss1/4