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

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.