\mathcal{N}-ideals of almost distributive lattices

In this article, we present the concept of an \mathcal{N}-ideal within the structure of an Almost Distributive Lattice (ADL). We demonstrate that the collection of \mathcal{N}-ideals constitutes a distributive lattice, which is distinct from and not a sublattice of the lattice of ideals in an ADL. Additionally, we define \mathcal{N}-lets in ADLs. We derive the necessary and sufficient conditions for an ideal to be classified as an \mathcal{N}-ideal using \mathcal{N}-lets. Finally, we establish the conditions required for an ADL to achieve the property of being soft relatively complemented.

کلیدواژه ها:

Almost Distributive Lattice (ADL) ، \mathcal{N}-ideal ، Dual dense element ، Soft relatively complemented ADL