Zero-Divisor Graphs, Commutative Rings of Quotients, and Boolean Algebras

Author

John D. LaGrange, University of Tennessee - Knoxville

Date of Award

5-2008

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

David F. Anderson

Committee Members

Michael Langston, Shashikant Mulay, Pavlos Tzermias

Abstract

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.

Recommended Citation

LaGrange, John D., "Zero-Divisor Graphs, Commutative Rings of Quotients, and Boolean Algebras. " PhD diss., University of Tennessee, 2008.
https://trace.tennessee.edu/utk_graddiss/393