N-ideals of almost distributive lattices

Document Type : Research Paper

Authors

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.

Abstract

In this article, we present the concept of an N-ideal within the structure of an Almost Distributive Lattice (ADL). We demonstrate that the collection of 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 N-lets in ADLs. We derive the necessary and sufficient conditions for an ideal to be classified as an N-ideal using N-lets. Finally, we establish the conditions required for an ADL to achieve the property of being soft relatively complemented.

Keywords


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