Involve: A Journal of Mathematics
- Volume 11, Number 2 (2018), 283-295.
Zero divisor graphs of commutative graded rings
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.
Involve, Volume 11, Number 2 (2018), 283-295.
Received: 30 September 2016
Revised: 17 March 2017
Accepted: 23 March 2017
First available in Project Euclid: 20 December 2017
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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