Some Properties of Modular n-Ideals of a Lattice

Abstract

An ideal M of a lattice L is called a modular ideal if for all ideals I, J∈I(L) with J ⊆ I , the relation I ∩(M ∨ J ) = (I ∩M)∨ J is satisfied. In this paper the authors have introduced the notion of modular n-ideals of a lattice. They have given several characterizations and properties of modular n-ideals when n is a neutral element in lattice L. They proved that the principal n-ideal n < s > is a modular nideal if and only if s ∧ n and s ∨ n are modular elements in (n] and [n) respectively. Finally, they have characterized modular n-ideals with the help of relative n-annihilators.