Vol. 8, No. 1, 2015

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
An exploration of ideal-divisor graphs

Michael Axtell, Joe Stickles, Lane Bloome, Rob Donovan, Paul Milner, Hailee Peck, Abigail Richard and Tristan Williams

Vol. 8 (2015), No. 1, 87–98
Abstract

Zero-divisor graphs have given some interesting insights into the behavior of commutative rings. Redmond introduced a generalization of the zero-divisor graph called an ideal-divisor graph. This paper expands on Redmond’s findings in an attempt to find additional information about the structure of commutative rings from ideal-divisor graphs.

Keywords
commutative ring with identity, radical ideal, zero-divisor graph, ideal-divisor graph
Mathematical Subject Classification 2010
Primary: 13M05
Milestones
Received: 19 February 2013
Revised: 25 June 2013
Accepted: 3 July 2013
Published: 10 December 2014

Communicated by Scott T. 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
Lane Bloome
Department of Mathematics
Millikin University
Decatur, IL 62522
United States
Rob Donovan
Department of Mathematics and Computer Science
Worcester State College
Worcester, MA 01602
United States
Paul Milner
Department of Mathematics
University of St. Thomas
St. Paul, MN 55105
United States
Hailee Peck
Department of Mathematics
Millikin University
Decatur, IL 62522
United States
Abigail Richard
Department of Mathematics
Miami University
Oxford, OH 45056
United States
Tristan Williams
Department of Mathematics
University of Iowa
Iowa City, IA 52242
United States