$mathcal{n}$-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.