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Zero divisor
graphs of commutative graded rings
Katherine Cooper and Brian Johnson
Vol. 11 (2018), No. 2, 283–295
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Abstract |
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We study a natural generalization of the zero divisor graph introduced by Anderson and Livingston to commutative rings graded by abelian groups, considering only homogeneous zero divisors. We develop a basic theory for graded zero divisor graphs and present many examples. Finally, we examine classes of graphs that are realizable as graded zero divisor graphs and close with some open questions. |
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Keywords
graded ring, zero divisor graph
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Mathematical Subject Classification 2010
Primary: 05C25, 13A02
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Milestones
Received: 30 September 2016
Revised: 17 March 2017
Accepted: 23 March 2017
Published: 17 September 2017
Communicated by Scott T. Chapman
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Authors |
| Katherine Cooper | |
| Department of Mathematics University of Kentucky Lexington, KY United States |
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| Brian Johnson | |
| Department of Mathematics Florida Gulf Coast University Fort Myers, FL United States |
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