Zero-Divisor Graphs, Commutative Rings of Quotients, and Boolean Algebras
Date of Award
Doctor of Philosophy
David F. Anderson
Michael Langston, Shashikant Mulay, Pavlos Tzermias
The zero-divisor graph of a commutative ring is the graph whose vertices are the nonzero zero-divisors of the ring such that distinct vertices are adjacent if and only if their product is zero. We use this construction to study the interplay between ring-theoretic and graph-theoretic properties. Of particular interest are Boolean rings and commutative rings of quotients.
LaGrange, John D., "Zero-Divisor Graphs, Commutative Rings of Quotients, and Boolean Algebras. " PhD diss., University of Tennessee, 2008.