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 |
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