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.
Identifer | oai:union.ndltd.org:UTENN/oai:trace.tennessee.edu:utk_graddiss-1454 |
Date | 01 May 2008 |
Creators | LaGrange, John D. |
Publisher | Trace: Tennessee Research and Creative Exchange |
Source Sets | University of Tennessee Libraries |
Detected Language | English |
Type | text |
Source | Doctoral Dissertations |
Page generated in 0.0014 seconds