The graph of zero-divisors of quadratic quotients of Rees algebras

Abstract

We study the graph of zero-divisors of a quadratic quotient of a Rees algebra. We provide conditions in order to determine its girth and diameter, extending several results regarding amalgamated duplications and Nagata’s idealization.

Keywords:

• Amalgamated duplication
• complete graph
• Nagata’s idealization
• zero-divisor graph

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 13A15
• Secondary: 05C25
• 13B02

Acknowledgements

The authors would like to thank the referee for his/her comments which helped to improve the presentation of the paper.

Additional information

Funding

The second author was partially supported by GNSAGA, by the project “Proprietà algebriche locali e globali di anelli associati a curve e ipersuperfici” PTR 2016-18—Dipartimento di Matematica e Informatica—Università di Catania, by the project PIACERI “PLGAVA—Proprietà locali e globali di anelli e di varietà algebriche” Dipartimento di Matematica e Informatica—Università di Catania, by the project “MTTAI—Metodi topologici in teoria degli anelli e loro ideali” Dipartimento di Matematica e Informatica—Università di Catania, and by the research program “Reducing complexity in algebra, logic, combinatorics—REDCOM” “Ricerca Scientifica di Eccellenza 2018” Fondazione Cariverona.