Reduced zero-divisor graphs of posets

Document Type : Research Paper

Authors

North Eastern Hill University

Abstract

This paper investigates properties of the reduced zero-divisor graph of a poset. We show that a vertex is an annihilator prime ideal if and only if it is adjacent to all other annihilator prime ideals and there are always two annihilator prime ideals which are not adjacent to a non-annihilator prime ideal. We also classify all posets whose reduced zero-divisor graph is planar or toroidal and the number of distinct annihilator prime ideals is four or seven.

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References

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History

  • Receive Date: 14 June 2016
  • Revise Date: 08 January 2018
  • Accept Date: 11 January 2018
  • Published Online: 01 June 2018

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