Involve: A Journal of Mathematics

  • Involve
  • Volume 11, Number 2 (2018), 283-295.

Zero divisor graphs of commutative graded rings

Katherine Cooper and Brian Johnson

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Abstract

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.

Article information

Source
Involve, Volume 11, Number 2 (2018), 283-295.

Dates
Received: 30 September 2016
Revised: 17 March 2017
Accepted: 23 March 2017
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1513775063

Digital Object Identifier
doi:10.2140/involve.2018.11.283

Mathematical Reviews number (MathSciNet)
MR3733958

Zentralblatt MATH identifier
1379.05051

Subjects
Primary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65] 13A02: Graded rings [See also 16W50]

Keywords
graded ring zero divisor graph

Citation

Cooper, Katherine; Johnson, Brian. Zero divisor graphs of commutative graded rings. Involve 11 (2018), no. 2, 283--295. doi:10.2140/involve.2018.11.283. https://projecteuclid.org/euclid.involve/1513775063


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