|
|||||
 |
|
|
|
|
|
Zero-divisor
ideals and realizable zero-divisor graphs
Michael Axtell, Joe Stickles and Wallace Trampbachls
Vol. 2 (2009), No. 1, 17–27
|
Abstract |
|
We seek to classify the sets of zero-divisors that form ideals based on their zero-divisor graphs. We offer full classification of these ideals within finite commutative rings with identity. We also provide various results concerning the realizability of a graph as a zero-divisor graph. |
Keywords
zero-divisor, graph, commutative ring
|
Mathematical Subject Classification 2000
Primary: 13A99
|
Milestones
Received: 10 July 2008
Revised: 16 July 2008
Accepted: 4 October 2008
Published: 18 March 2009
Communicated by Scott Chapman
|
Authors |
| Michael Axtell | |
| Department of Mathematics University of St. Thomas St. Paul, MN 55105 United States |
|
| Joe Stickles | |
| Department of Mathematics Millikin University Decatur, IL 62522 United States |
|
| Wallace Trampbachls | |
| Wabash Summer Institute in
Mathematics Crawfordsville, IN 47933 United States |
|
|
