$\mathcal{N}$-ideals of almost distributive lattices
نویسندگان
1 Department of Mathematics, Bapatla Engineering College, Bapatla, Andhra Pradesh, India-522 102.
2 Department of Mathematics, University of Gondar, Gondar, Ethiopia.
3 Department of Mathematics, Mohan Babu University, A. Rangampet, Tirupati, Andhra Pradesh, India-517 102.
doi
10.22034/as.2024.21809.1725چکیده
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.
