Corrigendum to: Zero divisor gragh of a lattice with respect to an ideal

TL;DR

This paper corrects errors in a previous study on zero divisor graphs of lattices with respect to ideals, providing counterexamples and revised proofs to ensure mathematical accuracy.

Contribution

It identifies and corrects specific inaccuracies in the prior work, including constructing a counterexample and reformulating proofs.

Findings

Counterexample disproves a claimed equality of ideal intersections.

Revised proofs clarify the correct conditions for theorems.

Highlights errors in the original analysis of zero divisor graphs.

Abstract

In this paper, we point out several errors in [M.Afkhami, K.Khashyarmanesh and K.Nafar, Zero divisor graph of a lattice with respect to an ideal, Beitr Algebra Geom (2015), 217-225.]. In the previous article, Afkhami claimed that the intersection of all prime ideals belonging to an ideal I of a distributive lattice L equals to I. In this corrigendum, a counterexample for this sentence is constructed. Afkhami demonstrate a counterexample to a certain theorem which satisfies the necessary and the sufficient condition of the theorem. On the other hand, we reform many proofs in Afkhami's article.