Zero-Divisor Graphs and Lattices of Finite Commutative Rings
نویسنده
چکیده
In this paper we consider, for a finite commutative ring R, the wellstudied 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. Acknowledgements: This paper is the result of a summer’s worth of undergraduate research at Millikin University and was funded by Millikin University’s Student Undergraduate Research Fund. The author would like to thank Dr. Joe Stickles for his guidance and advice throughout the development of this paper, Dr. Michael Axtell for his comments and suggestions, and Dr. James Rauff for his helpful input. Page 58 RHIT Undergrad. Math. J., Vol. 12, no. 1
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