Abstract

In this paper, we introduce and study the concept of Noether Skew Semi-Residuated Almost Distributive Lattices (Noether SSR ADLs). We define and examine the notion of principal elements within a Skew SemiResiduated Almost Distributive Lattice (SSR ADL) and establish several fundamental properties of these structures. Furthermore, we develop and prove significant results concerning the algebraic behavior of Noether SSR ADLs, culminating in the formulation and proof of the Fundamental Theorem of Noether SSR ADLs. These results provide new insights into the structural and order-theoretic characteristics of residuated lattice systems with skew and almost distributive properties.