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.

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Included in

Algebra Commons

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