Construction of Zero-Divisor Graph of a Hyperlattice with Respect to Hyperideals

Document Type : Research Paper

Authors

1 Department of Mathematics‎, ‎Manipal Institute of Technology‎, ‎Manipal Academy of Higher Education‎, ‎Manipal‎, ‎Karnataka‎, ‎India

2 Department of Chemistry‎, ‎Manipal Institute of Technology‎, ‎Manipal Academy of Higher Education‎, ‎Manipal‎, ‎Karnataka‎, ‎India

10.22052/ijmc.2024.253723.1774

Abstract

‎In this paper‎, ‎we define the zero-divisor graph of a meet-hyperlattice‎ with respect to a hyperideal‎. ‎We prove the diameter of a $P-$hyperlattice and Nakano‎ hyperlattice are at most 3 and 4 respectively‎. ‎We obtain that the zero-divisor‎ graph with respect to the intersection of two prime hyperideals is complete bipartite‎. ‎We‎ prove certain properties of these zero-divisor graphs with suitable examples.

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References

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Iranian Journal of Mathematical Chemistry
Volume 15, Issue 3
September 2024
Pages 123-135

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