Vol. 2, No. 1, 2009

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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