$σ$-Prime Spectrum of Almost Distributive Lattices (European Journal of Pure and Applied Mathematics, 2024)
For each $α$-ideal of an almost distributive lattice (ADL) to become a $σ$-ideal, a set of equivalent conditions is derived, which tends to result in a characterization of generalized Stone ADLs. On an ADL, a one-to-one correspondence is derived between the set of all prime $σ$-ideals of the ADL and the set of all prime $σ$-ideals of the quotient ADL. Finally, proved some properties of prime $σ$-ideals of a normal ADL topologically.
Keywords: almost distributive lattice (ADL); generalized Stone ADL; complemented ADL; relatively complemented ADL; normal ADL; minimal prime ideal; prime $σ$-ideal; prime $α$-ideal; compact space; non-dense